Prof. Dr. Ayşe Çiğdem Özcan

Hacettepe University

About Me

I am a Professor at the Department of Mathematics of the Faculty of Science of the University of Hacettepe in Ankara, Türkiye. I have been the head of the department from 2021 to 2024. I was an Editor-in-Chief at Hacettepe Journal of Mathematics and Statistics from 01.08.2018 to 30.07.2021. I am a member of the editorial board of the International Electronic Journal of Algebra and the Istanbul Journal of Mathematics.

My research interest lies in Ring and Module Theory, recently:

  • Lifting of some kind of elements, such as idempotents, regular and unit regular elements
  • Stable Range Condition

I supervised 2 PhD and 2 Master students. I have currently 1 master student.

CV

Education

  • High School: 1989, Şehit Mehmet Gönenç Lisesi, Bandırma
  • Bachelor: 1989-1993, Hacettepe University, Department of Mathematics
  • Master: 1993-1995, Hacettepe University, Department of Mathematics
  • PhD: 1995-1999, Hacettepe University, Department of Mathematics

    • Thesis Title: Characterizations of Some Rings by Small Modules and Decompositions of Modules

  • Associate Professor: November 2002, Hacettepe University, Algebra and Number Theory
  • Professor: April 2009, Hacettepe University, Algebra and Number Theory

Area of Interest

  • Ring and Module Theory:
  • Small modules
  • Z*(.) Functor
  • Torsion theories (co)generated by certain classes of modules
  • V-rings (rings in which every simple module is injective)
  • GV-rings (rings in which every simple singular module is injective)
  • Semiregular, Semiperfect, Perfect rings and modules
  • Harada rings and modules
  • Quasi-Frobenious (QF) rings
  • Clean Rings
  • Stable Range

Citations (Books)

  • J. Clark, C. Lomp, N. Vanaja, R. Wisbauer, Lifting Modules, Supplements and Projectivity in Module Theory, Birkhäuser Basel, 2006. (Ref: [7], [277], [278], [279])
  • A. Tuganbaev, Rings Close to Regular, Kluwer Academic Publishers, 2002. (Ref: [312])

Conferences Abroad

  • 12-17 January 1998, Murcia University, Spain "Euroconference Interactions Between Ring Theory and Representations of Algebras" (TÜBİTAK BDP Supported).
  • January 1998 - June 1998, Glasgow University, England (TÜBİTAK BDP Supported).
  • 25-28 March 1999, Ohio University, USA. "International Conference on Algebra and Its Applications" (TÜBİTAK supported).
  • 14-18 August 2000, Ovidius University, Constanta, Romania "The Euroconference on Rings, Modules and Representations".
  • 8-10 September 2006, Porto University, Porto, Portugal, "International Conference on Modules and Comodules" dedicated to Robert Wisbauer.
  • 10-15 September 2007, "The Fifth China-Japan-Korea International Symposium on Ring Theory", Tokyo, Japan.
  • 16-19 September 2008, "International Conference on Rings and Modules in honour of Patrick F. Smith's 65th Birthday", Lisbon, Portugal.
  • 29 June-2 July 2009, "Noncommutative Rings and Their Applications", Lens, France.
  • 25-27 May 2012, The 31st Ohio State-Denison Mathematics Conference, Columbus, Ohio.
  • 3-7 June 2013, Recent Trends in Rings and Algebras, Murcia, Spain.
  • 14-20 July 2013, Classical Aspects on Ring Theory and Module Theory, Bedlewo, Poland.
  • 8-11 June 2015, Noncommutative rings and their applications, IV, Lens, France.
  • 18-25 May 2018, Padova University, Padova, Italy.
  • 05-07 July 2021, "Noncommutative Rings and Their Applications VII (Dedicated to Tariq Rizvi)", Lens, France.(Online)
  • 10-12 May 2024, XXXVI Ohio State-Denison Mathematics Conference (Dedicated to the memory of Tariq Rizvi), Columbus, Ohio. (Online)
  • 30 June-03 July 2025, "Noncommutative Rings and Their Applications IX", Lens, France.(Online-Speaker)

Conferences at Home

  • 19-23 May 1999, Antalya Algebra Days I, TÜBİTAK Mathematics Working Group, Antalya.
  • 17-21 May 2000, Antalya Algebra Days II, Antalya.
  • 6-9 September 2000, XIII. National Mathematics Symposium, İstanbul.
  • 15-20 May 2001, Antalya Algebra Days III, Antalya.
  • 22-26 May 2002, Antalya Algebra Days IV, Antalya.
  • 28 May-1 June 2003, Antalya Algebra Days V, Antalya.
  • 23-26 August 2004, XVII. National Mathematics Symposium, Abant İzzet Baysal University, Bolu.
  • 17-20 May 2005, Antalya Algebra Days VII, Antalya.
  • 5-8 September 2005, XVIII. National Mathematics Symposium, İstanbul Kültür University.
  • 17-21 May 2006, Antalya Algebra Days VIII, Antalya.
  • 28 May - 1 June 2008, Antalya Algebra Days X, Antalya.
  • 18-22 August 2008, Rings and Modules, Hacettepe University, Ankara.
  • 20-24 May 2009, Antalya Algebra Days XI, Antalya.
  • 19-22 May 2010, Antalya Algebra Days XII, Antalya.
  • 3-4 June 2010, 5th Ankara Mathematics Days, TOBB University of Economics and Technology, Ankara.
  • 2-3 June 2011, 6th Ankara Mathematics Days, Hacettepe University, Ankara.
  • 20-23 July 2011, The 24th International Conference of Jungjeon Mathematical Society, Selçuk University, Konya.
  • 31 May-1 June 2012, 7th Ankara Mathematics Days, Bilkent University, Ankara.
  • 11-15 June 2012, Workshop on Ring Theory, Karabük University, Karabük.
  • 23-25 May 2013, 12th Mathematics Symposium: Mathematics in Society, Hacettepe University.
  • 24-28 June 2013, Ring and Module Workshop, İzmir Institute of Technology, Urla, İzmir.
  • 12-15 August 2013, International Conference on Algebra, Balıkesir University, Burhaniye, Balıkesir.
  • 1-5 June 2015, 4th Ring and Module Workshop, Hacettepe University, Ankara.
  • 22-23 April 2016, 4th Cemal Koç Algebra Days, METU, Ankara.
  • 30 May-3 June 2016, 5th Ring and Module Workshop, Hacettepe University, Ankara.
  • 3-7 July 2017, 6th Ring and Module Workshop, Dokuz Eylül University, İzmir. Invited Speaker.
  • 29 January-2 February 2018, Algebra Workshop, Afyon Kocatepe University, Afyon.
  • 20-24 June 2018, New Trends in Rings and Modules, Gebze Technical University, Gebze.
  • 27 April 2024, 8th Cemal Koç Algebra Days, Hacettepe University, Ankara.
  • 1-4 July 2024, 10th Workshop on Ring, Module and Algebra, Hacettepe University, Ankara.
  • 02 May 2025, 9th Cemal Koç Algebra Days, Ege University, İzmir.
  • 24-26 June 2025, Second Joint IIIMT Algebra Forum Conference, Karaman, Türkiye (Invited Speaker).

Seminars

  • 28 February 2008, Bolu Abant İzzet Baysal University, Bolu, Türkiye
  • 26 March 2010, Bilkent University, Ankara, Türkiye
  • 19 October 2011, Hacettepe University, Ankara, Türkiye
  • 24 May 2018, Padova University, Padova, Italy
  • 11 May 2025, 16. Bahar Matematik Buluşması, Bilkent University, Ankara, Türkiye

Committees

  • 12th Mathematics Symposium, Hacettepe University, Sıhhıye Campus, Cultural Center, 23-25 May 2013, Ankara. (Scientific Committee)
  • International Conference on Algebra in Honour of Patrick Smith and John Clark's 70th Birthdays, Balıkesir, Türkiye, 12-15 August 2013. (Organizing Committee and Scientific Committee)

Supervision

Master's:

  • Pınar Aydoğdu, "Generalization of Semiregular and Semiperfect Rings", 2004-2006.
  • Meltem Altun, "Some Ring and Module Structures Defined by Morphisms", 2010-2013.

PhD:

  • Pınar Aydoğdu, "A Study on Perfect and Regular Rings", 2007-2011.
  • Meltem Altun, "A Study on Direct Summand Submodules in Noncommutative Rings", 2013-2018.

Editorial

  • International Electronic Journal of Algebra (2007-)
  • International Journal of Mathematics and Mathematical Sciences (Guest Editor)
  • Hacettepe Journal of Mathematics and Statistics (01.08.2018-30.07.2021) (Editor-in-Chief)
  • Istanbul University Science Faculty The Journal of Mathematics, Physics and Astronomy (12.2018-) (Field Editor)

Refereeing

  • Turkish J. Math., Hacettepe J. Math. Stat., Bull. Korean Math. Soc, Algebra Colloquium, Bull. Malaysian Math. Soc., Asian-European J. Math., Bull. Iranian Math. Soc., J. Algebra and its Applications

Administrative Duties

  • Head of Algebra and Number Theory Department (2009-2018)
  • Head of Mathematics Department (08.06.2021-)

Publications

2020 – On lifting of stable range one elements – (M. Altun-Ozarslan, A.C. Ozcan), J. Korean Math. Soc, 57(3), 793-807, 2020.
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2018 – C4- and D4-Modules via perspective direct summands – (M. Altun-Ozarslan, Y. Ibrahim, A.C. Ozcan, M.F. Yousif), Comm. Algebra, 46(10), 4480-4497, 2018.
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2018 – Primitive submodules, co-semisimple and regular modules – (M. Medina-Barcenas, A.C. Ozcan), Taiwanese J. Math., 22(3), 454-565, 2018.
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2018 – Comorphic rings – (W.K. Nicholson, M. Alkan, A.C. Ozcan), J. Algebra and Its Applications, Vol.17 No. 4, 1850075, 21 pp., 2018.
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2017 – On internally cancellable rings – (M. Altun, A.C. Ozcan), J. Algebra and Its Applications, Vol.16, No. 5, 1750117(12 pages), 2017.
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2017 – Strongly Nil-*-clean rings – (H. Chen, A. Harmanci, A. C. Ozcan), J. Algebra Combinatorics Discrete Structure and Appl., Special Issue: Noncommutative Rings and Their Appl., 4(2), 155-164, 2017.
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2016 – On Jacobson and nil radicals related to polynomial rings – (Tai Keun Kwak, Yang Lee, A. C. Ozcan) J. Korean Math. Soc., 53(2), 415-431, 2016.
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2014 – Strongly J-clean rings with involutions – (H. Chen, A. Harmanci, A. C. Ozcan), Ring theory and its applications, 33-44, Contemp.Math., 609, Amer. Math. Soc., Providence, RI, 2014.
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2013 – On a class of uniquely (strongly) clean rings – (O. Gurgun, A. C. Ozcan), Turkish Journal of Mathematics, DOI: 10.3906/mat-1209-9, 2013.
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2012 – Rings close to semiregular – (P. Aydogdu, A. C. Ozcan, Y. Lee) J. Korean Math. Soc., 49(3), 605-622, 2012.
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2011 – Fleury's spanning dimension and chain conditions on non-essential elements in modular lattices – (C. Lomp, A. C. Ozcan), Colloquium Mathematicum, 124(1), 133-144, 2011.
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2011 – Chain conditions on non-summands – (P. Aydogdu, A.C. Ozcan, P.F. Smith), J. Algebra and Its Applications, 10(3), 475-489, 2011.
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2011 – Strong lifting splits – (M. Alkan, W.K. Nicholson, A. C. Ozcan), J. Pure and Appl. Algebra, 215(8), 1879-1888, 2011.
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2010 – Almost perfect modules – (P. Aydogdu, A.C. Ozcan), Glasgow Math. J., 52A, 33–40, 2010.
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2010 – A generalization of semiregular and almost principally injective rings – (A.C. Ozcan, P. Aydogdu), Algebra Colloquium 17 (Spec 1) 905-916, 2010.
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2009 – On μ-essential and μ-M-singular modules – Ring Theory 2007 (the Fifth China-Japan-Korea Conference, Tokyo, Japan) World Sci. Publ., Hackensack, NJ, 272-283, 2009.
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2008 – Semi co-Hopfian modules and semi Hopfian modules – (with P. Aydogdu), East West J. Math., 10(1), 55-70, 2008.
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2008 – A generalization of projective covers – (with M. Alkan, W.K. Nicholson), J. Algebra, 319, 4947-4960, 2008.
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2008 – On some injective modules in σ[M] – (with D.Keskin Tutuncu, M.F. Yousif) Modules and Comodules, Trends in Mathematics, 313-329, 2008.
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2008 – δ-M-small and δ-Harada modules – (with T. Kosan), Comm. Algebra, 36, 423-433, 2008.
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2008 – A generalization of semiregular and semiperfect modules – (with P. Aydoğdu), Algebra Colloquium, 15(4), 667-680, 2008.
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2007 – The torsion theory cogenerated by δ-M-small modules and GCO-modules – Comm. Alg. 35, 623-633 (2007).
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2006 – Duo modules – (with A. Harmanci, P.F. Smith), Glasgow Math. J., 48(3) 533-545 (2006).
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2006 – Semiperfect modules with respect to a preradical – (with M. Alkan), Comm. Algebra, 34, 841-856 (2006).
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2005 – Characterization of modules and rings by the summand intersection property and the summand sum property – (with A. Hamdouni, A.Harmancı), JP Jour.Algebra, Number Theory & Appl. 5(3), 469-490 (2005).
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2004 – Semiregular modules with respect to a fully invariant submodule – (with M. Alkan) Comm. Alg., 32(11) 4285-4301 (2004).
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2003 – The torsion theory generated by M-small modules – (with A. Harmancı) Alg. Coll., 10(1) 41-52 (2003).
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2002 – On GCO-modules and M-small modules – Commun. Fac.Sci.Univ. Ank. Series A1, 51 (2), 25- 36, (2002).
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2002 – Direct sum of modules having (S*) – East West J. Math., 4(1), 157-165, (2002).
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2002 – The Z* functor for rings whose primitive images are artinian – (with P.F.Smith) Comm. Alg. 30(10) 4915-4930 (2002).
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2002 – Modules with small cyclic submodules in their injective hull – Comm.Alg. 30(4) 1575-1589 (2002).
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2000 – On rings which every module with (S*) is extending – Ring Modules and Representations- Constanta (Romanya) 2000, Analele Stiintifice ale Universitatii, Ovidius, Constanta, Seria Matematica, 8(2) 85-98 (2000).
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2000 – Modules having *-radical – Algebra and its applications (Athens, Ohio,1999) 439-449, Contemp. Math., 259,Amer. Math. Soc., Providence,RI (2000).
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2000 – On a class of modules – Publ. Math. Debrecen, 57 (3-4), 269-275 (2000).
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1998 – Modules with zero radical of their injective hull – Hacettepe Bulletin of Natural Sciences and Engineering, 27, 45-49 (1998).
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1998 – Some characterizations of V-modules and rings – Vietnam J.Math., 26 (3), 253-258 (1998).
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1997 – Characterization of some rings by functor Z*(.) – A. Ç. Özcan, A. Harmancı, Turkish Journal of Mathematics 21, 325–331 (1997).
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1996 – On prime submodules – (with D. Keskin, Y. Tıraş) Far East J.Math.Sci. 4(2) 163-168 (1996).
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All Publications

Teaching

Courses Taught

Undergraduate:

MTK 161 Soyut Matematik I
MTK 162 Soyut Matematik II
MTK 241 Doğrusal Cebir I
MTK 242 Doğrusal Cebir II
MTK 244 Soyut Cebir I
MTK 341 Soyut Cebir II
MTK 440 Cebirde Seçme Konular
MTK 495 Matematikte Seçme Konular

Graduate - PhD:

MAT 541 Cebir I
MAT 643 Halka ve Modül Kuramı
MAT 644 Grup Halkaları
MAT 646 Değişmeli Cebir II
MAT 647 Cebirde Seçme Konular I
MTK 745 Homolojik Cebir I

Service Courses:

MAT 113 Matematik
MAT 107 Mathematics I
MAT 108 Mathematics II
MAT 145 Matematik I
MAT 146 Matematik II
MAT 225 Advanced Calculus I (Calculus, R.A. Adams)
MAT 226 Advanced Calculus II (Differential Equations, S.L. Ross)
MAT 238 Introduction to Engineering Mathematics (Calculus, R.A. Adams)
MAT 254 Temel Doğrusal Cebir
İMÖ 203 Doğrusal Cebir I
İMÖ 204 Doğrusal Cebir II
İMÖ 303 Cebire Giriş
MTÖ 110 Soyut Matematik

Contact

Hacettepe University

Hacettepe Üniversitesi Beytepe Yerleşkesi Matematik Fakültesi

Phone: 0 312 297 78 50/133

Fax: 0 312 299 20 17

Email: ozcan@hacettepe.edu.tr