Brief CV

• 2019-now Associate Professor, Universidade do Porto
• 2019 Diplom Informatik, Fernuni-Hagen, grade: “mit Auszeichnung”
• 2011 Agregação (Habilitation), Universidade do Porto
• 2002-2019 Professor Auxiliar, Universidade do Porto (since 2007 Portuguese Civil Servant)
• 2002 PhD Mathematics (Dr.Rer-Nat), Universität Düsseldorf, grade: “magna cum laude”
• 1998-2002 Assistent, Universidade do Porto
• 1997-1998 Teaching Assistant, University of Wisconsin-Milwaukee
• 1997 Master of Science, University of Glasgow
• 1997 Diplom Mathematik, Universität Düsseldorf, grade: “mit Auszeichnung”
• 1995 Tutor, University of Glasgow
• 1994+1995 Software Developer, Scientific Center IBM, Heidelberg
• 1993-1995 Tutor, Universität Düsseldorf + Fernuni-Hagen
• 1991 Programmer, CoCoNet Düsseldorf
• 1990 Study of Mathematics, Universität Düsseldorf
• 1989-1990 Zivildienst, Sozialamt Düsseldorf
• 1989 Abitur, Mataré-Gymnasium Meerbusch

Teaching

Modules for which I was responsible at the University of Porto since 2002.

• M1026 Linear Algebra and Analytic Geometry 2, BSc Math.
• M3015 Number Theory and its applications, BSc Math ( notes)
• M3001 Applied Abstract Algebra, BSc Math.
• M3010 Computational Mathematics (Gröbner Bases), BSc Math.
• M341 Galois Theory, BSc Math.
• M342 Computer Algebra, BSc Math.
• M442 Rings and Modules, MSc Math.
• M4075 Algebra , MSc Math.
• M4029 Commutative Algebra, MSc Math.
• M4081 Algebraic Coding Theory, MSc Math.
• M561 Noncommutative Algebra, PhD Math.( notes)
• M558 Quantum groups, PhD Math.
• Introduction to abstract Algebra, BSc Math.
• Linear Algebra II, BSc Comp. Science
• Information- and Coding Theory,BSc Math.
• M191 Mathematics I, BSc Comp. Science
• Analysis I, BSc Comp. Science
• Calculus II, BSc Comp. Science
• Computers in the classroom, BSc Math.

Lectures held at other universities.

• Intermediate Algebra, Universität Wisconsin-Milwaukee, 1997-1998
• Exercises for linear algebra II (for Prof. Wisbauer), Düsseldorf, 1997
• Tutorials in Maths for Engeneering students, University Glasgow, 1995/96

Mini-courses

• Lectures on Artinian and quasi-Frobenius rings (8 hours), Izmir Institute of Technology, Izmir, Turkey (2022)
• Introduction to affine cellular algberas (4 hours), Southwest Jiaotong University, Chengdu, China (2017)
• Hopf Ore Extensions (8 hours), UFRGS, Porto Alegre, Brazil (2014)
• Introduction to Hopf algebra actions (4 hours), University of Warsaw, Poland (2010)
• Separable Algebras (6 hours), Dokuz Elyul University, Izmir, Turkey (2008)
• Partial entwining structures (6 hours), UFRGS, Porto Alegre, Brazil (2006)

Publications

Papers

1. Essential Quasi-Duo Rings (with Mohamed Yousif and Yiqiang Zhou), accepted for publications in "Proceedings of the conferences: NonCommutative Rings and their Applications, VIII and Quadratic Forms, Rings and Codes", ed. Michela Ceria, Steven Dougherty, Alberto Facchini, Ahmed Laghribi, Andre Leroy, Sergio Lopez-Permouth, and Cesar Polcino Milies, Contemporary Mathematics, AMS (2025)
2. On Hypercyclic Rings (with Mohamed Yousif and Yiqiang Zhou), J. Algebra Appl. 23 (2024), no. 8, Paper No. 2550051 ( preprint)
3. Dual Kasch Rings (with E.Büyükasik), J. Algebra Appl. 2450225 (2024) (preprint)
4. Locally Finite Representations Over Noetherian Hopf algebras (with C.Hatipoglu), Proc. Amer. Math. Soc. 150 (2022), 1903-1923 ( preprint)
5. Stable range one for rings with central units (with P. Carvalho and J.Matczuk), Commun. Algebra 48, No. 11, 4767-4773 (2020). preprint
6. A note on simple modules over quasi-local rings (with P.Carvalho and P.F.Smith), Int. Elect. J. Algebra 24 (2018) 91-106
7. Panov's theorem for weak Hopf algebras (with A.Sant'Ana and R.Leite dos Santos), Contemp. Math. AMS (2019) (preprint)
8. Differential smoothness of skew polynomial rings (with Tomasz Brzeziński), Journal of Pure and Applied Algebra 222(9) (2018) 2413-2426, arXiv:1609.04055
9. A counterexample for a problem on quasi Baer modules Taiwanese J. Math. 21 (2017), no. 6, 1277–128, arXiv:1605.02297
10. Ring theoretical properties of affine cellular algebras (with Paula A. A. B. Carvalho, Steffen Koenig and Armin Shalile), Journal of Algebra (2017), arXiv:1609.01771
11. A note on a paper by Cuadra, Etingof and Walton (with Deividi Pansera), Communications in Algebra (2017), arXiv:1506.07766
12. A note on semicentral idempotents (with Jerzy Matczuk), Communications in Algebra 45 no. 6 (2017) 2735 - 2737, arXiv:1605.02360
13. On Topological Lattices and their Applications to Module Theory (with Jawad Abuhlail), J. Algebra Appl. 15 (2016), no. 3, 1650046, 21 pp. arXiv:1305.4578
14. (survey) On the semiprime smash product question in "Proceedings of the International Conference on Noncommutative Rings and their Applications" Edited by: S. Dougherty, A. Facchini, A. Leroy, E. Puczylowski, and P. Solé, Contemporary Mathematics Volume 634, AMS, 2015 (corrected version)
15. Injective hulls of simple modules over differential operator rings (with Paula Carvalho and Can Hatipoglu), Communications in Algebra 43 (2015), 4221-4230 arXiv:1211.2592
16. A note on dimension modules (with Edmund Puczylowski), Communications in Algebra 43 (2015) 2267–2271
17. Endomorphism rings of modules over prime rings (with M.Baziar), Taiwanese Journal of Mathematics 19 (2015), 953-962
18. (survey) On the notion of 'retractable modules' in the context of algebras in "Proceedings of International Conference on Algebra in Honour of Patrick Smith and John Clark's 70th Birthdays", Palestine Journal of Mathematics 3(Spec 1), 342–354 (2014)
19. Integral Calculus on Quantum Exterior Algebras (with Serkan Karaçuha) Int. J. Geom. Methods Mod. Phys. 11, 1450026 (2014), DOI: 10.1142/S0219887814500261 arXiv:1302.5216
20. On the notion of strong irreducibility and its dual (with J.Abuhlail) Journal of Algebra and its Applications 12,1350012 (2013), arXiv:1207.4227
21. Injective hulls of simple modules over finite dimensional nilpotent complex Lie superalgebras (with C.Hatipoglu), Journal of Algebra, Volume 361 (2012), 79-91
22. Quantum Groupoids acting on semiprime algebras (with I.Borges) Advances in Mathematical Physics (2011) 9pp
23. Fleury's spanning dimension and chain conditions on non-essential elements in modular lattices (with A.C.Ozcan) Colloquium Mathematicum 124 (2011), 133-144
24. Irreducible Actions and Compressible Modules (with I.Borges), Journal of Algebra and its Applications 10(1), 101-117 (2011), arXiv:1003.4108
25. Injective Modules over Down-Up algebras (with Paula A.A.B. Carvalho and Dilek Pusat-Yilmaz), Glasgow Mathematical Journal 52A 53-59 (2010)
26. Non-commutative integral forms and twisted multi-derivations (with T.Brzezinski and L.El Kaoutit), Journal of Noncommutative Geometry 4(2) 281-312 (2010)
27. When δ-semiperfect rings are semiperfect. (with E.Büyükasik), Turkish Journal of Mathematics 34, 317 – 324 (2010).
28. Rings whose modules are weakly supplemented are perfect. Applications to certain ring extensions. (with E.Büyükasik), Mathematica Scandinavia 105 (2009), 25-30
29. All hereditary torsion theories are differential. (with J. van den Berg), Journal of pure and applied Algebra 213 (2009), 476-478
30. Comparability, Distributivity and non-commutative φ-rings (with A.Sant'ana), in "Groups, Rings and Group Rings" Edited by: Antonio Giambruno, César Polcino Milies and Sudarshan K. Sehgal, Contemporary Mathematics 499, 205-218, AMS (2009)
31. Regular and biregular module algebras. Arabian Journal for Science and Engineering 33 (2c), 351-364 (2008)
32. Duality for partial group actions International Electronic Journal of Algebra 4 53-62 (2008)
33. On a recent generalization of semiperfect rings. (with E.Büyükasik) Bulletin of the Australian Mathematical Society 78(2), 317-325 (2008)
34. Covering coalgebras and dual non-singularity (with V.Rodrigues), Applied Categorical Structures 16(2008), 195-211
35. Chain and Distributive Coalgebras (with A.Sant'Ana), Journal of Pure and Applied Algebra, 211(3), 581-595 (2007)
36. (survey) Kostia Beidar's contribution to module and ring theory (with R.Wisbauer), in "Rings and Nearrings - a Volume in Memory of the work of Kostia Beidar", M.Chebotar; K.WenFong; L. PjekHwee; F.Yuen (eds.), p 73-93, Walter de Gruyter 2007
37. A note on extending Hopf algebra actions to rings of quotients Beiträge zur Algebra und Geometrie 47(1), 137-146 (2006)
38. An example of an indecomposable module without non-zero hollow factor modules Turkish Journal Math 31(4)(2006), 1-5
39. τ-complemented and τ-supplemented modules (with K.Al-Takhman and R.Wisbauer), Algebra and Disrete Mathematics 3 (2006) 1-15
40. A central closure construction for certain extensions. Applications to Hopf actions Journal of Pure and applied Algebra, 198 (1-3), 297-316 (2005)
41. Prime elements in partially ordered groupoids applied to modules and Hopf algebra actions. Journal of Algebra and its Applications, 4(1), 77-98 (2005)
42. Integrals in Hopf algebras over rings Communications in Algebra, 32(12), 4687-4711 (2004)
43. When is a smash product semiprime? A partial answer Journal of Algebra 275(1), 339-355 (2004)
44. Projective modules with semilocal endomorphism ring.(with M.F. Nasrutdinov and I.I. Sakhayev) Russian Mathematics 46(8), 20-26 (2002) - “On LE-lifting modules”, (with D.Keskin) Vietnam Mathematical Journal 30(2), 167-176 (2002)
45. A remark on a theorem of Y.Kurata” Hokkaido Journal of Mathematics 30 (3), 645-648 (2001)
46. A note on prime modules (with A.J.Pena P.), Divulgaciones Mathematica 8(1), 31-42 (2000)
47. The splitting of the dual Goldie torsion theory in "Algebra and Its Applications" Edited by: D. V. Huynh, S. K. Jain, and S. R. López-Permouth, Contemporary Mathematics 259, 377-386 (2000)
48. Semilocal modules and rings Communications in Algebra 27(4), 1921-1935 (1999)
49. Modules whose small submodules have Krull dimension Journal of Pure and applied Algebra 133(1-2), 197-202 (1998)

Theses and Books

• Untere Schranken für das Erkundungsproblem, Diplomarbeit Informatik 2019, Fernuniversität Hagen
• Lifting modules - Supplements and Projectivity in Module Theory with J.Clark, N.Vanaja, Robert Wisbauer, Frontiers in Mathematics, Birkhäuser (2006)
• Primeigenschaften von Algebren in Modulkategorien über Hopfalgebren PhD thesis, Heinrich-Heine Universität Düsseldorf, 2002
• On dual Goldie dimension , MSc thesis, University of Glasgow, 1997 and Diplomarbeit, Heinrich-Heine Universität Düsseldorf, 1997

Chapters in Books

• Sistemas de verificação de dígitos(com Sandra Pires) in Treze Viagens pelo Mundo da Matemática, C.Sá and J.Rocha (eds.), chapter 12, Universidade do Porto (2010)

Unpublished Notes and Reports

• Ring theoretic aspects of weak Hopf actions Preprint MPIM2009-30, Max-Planck Institut für Mathematik, Bonn 2009
• Idempotent submodules preprint CMUP 2006-38

Supervision

Doctoral students

• Ricardo Leite dos Santos, Extensões de Ore e Álgebras de Hopf Fracas (co-supervision with Alveri Sant'Ana, UFRGS), 2014-2017
• Deividi Pansera, On semisimple Hopf actions, 2014-2017
• Serkan Karaçuha, Aspects of Non-commutative Differential Geometry, 2011-2015
• Can Hatipoglu, Injective Hulls of simple modules over some Noetherian rings, 2010-2013
• Marcin Szamotulski, ”Galois Theory for H-extensions”, (co-supervision with Roger Picken from IST), 2011-2013
• Inês Borges, ”Actions of weak Hopf algebras”, 2005-2011

Master students

• Patrícia Reis dos Reis, Teorema de Extensão de MacWilliams, 2017/2018
• Gjermund Johansen, Primitivity of Skew Polynomial Rings, 2017/2018
• Manuel Martins, Hopf Algebras and Ore Extensions (co-supervised with Paula Carvalho), 2015/2016
• Miguel Ângelo Couto, Anéis primitivos e Teorema da Densidade (Mestrado em Matemárica), 2012/2013
• Orlando Sá Couto ”Isometrias em Teoria de Códigos” (Mestrado em Matemática para Professores), 2009/2010
• Bruno Jesus ”Limites de códigos” (Mestrado em Engenharia de Matemática), 2005/2006
• Sandra Mónica, Curvas Algébricas e Códigos Geométricos (Mestrado em Ensino de Matemática), 2004/2005
• Dora Araújo “Um teorema com o Tangram” (Mestrado em Ensino de Matemática), 2003-2005

Students in other programs

• Program Novos Talentos em Matemática, Fundação Calouste Gulbenkian
  • Maria Ana Barbosa, "Zero-Divisor Problem in group rings", 2018/19 (together with P. Carvalho)
  • Manuel Martins, “Rational equivalence of the quantum plane”, 2013/14 (together with P. Carvalho)
  • Artur Amorim, “Characterisation of nilpotent Lie algebras”, 2010/11
  • Sérgio Dias, “Van der Waerden numbers and Ramsey theory”, 2007/2008
  • Lara Lacerda, “Neural networks”, Program “Novos Talentos em Matemática”, 2003/2004
• João Pedro Cunha, high-school student of the program SigMa temático, 2006/2007
• Jorge Vitoria, “Plano quântico e o seus simetrias”, research initiation program “Bolsas de iniciação científica”, 2004/2005 (together with P. Carvalho)

Postdoctoral Researcher

• Zahra Nazemian, Yazd (Iran), 2016/2017
• Tuğba Güroğlu, Celal Bayar University (Turkey), 2012
• Engin Büyükaşık, Izimir Institute of Technology (Turkey), 2007
• Alveri Sant’Ana, Universidade Federal do Rio Grande do Sul (Brazil), 2006/2007
• Vigínia Rodrigues, Universidade Federal de Santa Clara (Brazil), 2005/2006