Papers

  1. Differential smoothness of skew polynomial rings (with Tomasz Brzeziński), Journal of Pure and Applied Algebra, in press (2017), arXiv:1609.04055
  2. A counterexample for a problem on quasi Baer modules, accepted in Taiwanese Journal of Mathematics, arXiv:1605.02297
  3. 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
  4. A note on a paper by Cuadra, Etingof and Walton (with Deividi Pansera), Communications in Algebra (2017), arXiv:1506.07766
  5. A note on semicentral idempotents (with Jerzy Matczuk), Communications in Algebra 45 no. 6 (2017) 2735 - 2737, arXiv:1605.02360
  6. 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
  7. 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
  8. A note on dimension modules (with Edmund Puczylowski), Communications in Algebra 43 (2015) 2267–2271
  9. Endomorphism rings of modules over prime rings (with M.Baziar), Taiwanese Journal of Mathematics 19 (2015), 953-962
  10. 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
  11. On the notion of strong irreducibility and its dual (with J.Abuhlail) Journal of Algebra and its Applications 12,1350012 (2013), arXiv:1207.4227.
  12. Injective hulls of simple modules over finite dimensional nilpotent complex Lie superalgebras (with C.Hatipoglu), Journal of Algebra, Volume 361 (2012), 79-91
  13. Quantum Groupoids acting on semiprime algebras (with I.Borges) Advances in Mathematical Physics (2011) 9pp
  14. Irreducible Actions and Compressible Modules (with I.Borges), Journal of Algebra and its Applications 10(1), 101-117 (2011), arXiv:1003.4108
  15. Injective Modules over Down-Up algebras (with Paula A.A.B. Carvalho and Dilek Pusat-Yilmaz), Glasgow Mathematical Journal 52A 53-59 (2010)
  16. Non-commutative integral forms and twisted multi-derivations (with T.Brzezinski and L.El Kaoutit), Journal of Noncommutative Geometry 4(2) 281-312 (2010)
  17. When δ-semiperfect rings are semiperfect. (with E.Büyükasik), Turkish Journal of Mathematics 34, 317 – 324 (2010).
  18. All hereditary torsion theories are differential. (with J. van den Berg), Journal of pure and applied Algebra 213 (2009), 476-478
  19. 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)
  20. Regular and biregular module algebras. Arabian Journal for Science and Engineering 33 (2c), 351-364 (2008)
  21. Duality for partial group actions, International Electronic Journal of Algebra 4 53-62 (2008)
  22. On a recent generalization of semiperfect rings. (with E.Büyükasik) Bulletin of the Australian Mathematical Society 78(2), 317-325 (2008)
  23. Covering coalgebras and dual non-singularity (with V.Rodrigues), Applied Categorical Structures 16(2008), 195-211
  24. Chain and Distributive Coalgebras (with A.Sant'Ana), Journal of Pure and Applied Algebra, 211(3), 581-595 (2007)
  25. A note on extending Hopf algebra actions to rings of quotients, Beiträge zur Algebra und Geometrie 47(1), 137-146 (2006)
  26. τ-complemented and τ-supplemented modules (with K.Al-Takhman and R.Wisbauer), Algebra and Disrete Mathematics 3 (2006) 1-15
  27. A central closure construction for certain extensions. Applications to Hopf actions, Journal of Pure and applied Algebra, 198 (1-3), 297-316 (2005)
  28. Prime elements in partially ordered groupoids applied to modules and Hopf algebra actions., Journal of Algebra and its Applications, 4(1), 77-98 (2005)
  29. Integrals in Hopf algebras over rings, Communications in Algebra, 32(12), 4687-4711 (2004)
  30. When is a smash product semiprime? A partial answer, Journal of Algebra 275(1), 339-355 (2004)
  31. “Projective modules with semilocal endomorphism ring.”(with M.F. Nasrutdinov and I.I. Sakhayev) Russian Mathematics 46(8), 20-26 (2002)
  32. “On LE-lifting modules”, (with D.Keskin) Vietnam Mathematical Journal 30(2), 167-176 (2002)
  33. “A remark on a theorem of Y.Kurata”, Hokkaido Journal of Mathematics 30 (3), 645-648 (2001)
  34. A note on prime modules (with A.J.Pena P.), Divulgaciones Mathematica 8(1), 31-42 (2000)
  35. 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)
  36. Semilocal modules and rings, Communications in Algebra 27(4), 1921-1935 (1999)
  37. Modules whose small submodules have Krull dimension, Journal of Pure and applied Algebra 133(1-2), 197-202 (1998)

Survey Papers in conference proceedings

  1. (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
  2. (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)
  3. (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

Theses and Books

  1. Lifting Modules “Lifting modules - Supplements and Projectivity in Module Theory” with J.Clark, N.Vanaja, Robert Wisbauer, Frontiers in Mathematics, Birkhäuser (2006)
  2. Primeigenschaften von Algebren in Modulkategorien über Hopfalgebren, PhD thesis, Heinrich-Heine Universität Düsseldorf, 2002
  3. On dual Goldie dimension , MSc thesis, University of Glasgow, 1997 and Diplomarbeit, Heinrich-Heine Universität Düsseldorf, 1997

Chapters in Books

  1. 13 Viagens Sistemas de verificação de dígitos (com Sandra Pires) in “13 Viagens pelo Mundo da Matemática”, C.Sá and J.Rocha (eds.), chapter 12, Universidade do Porto (2010)

Unpublished Notes and Reports

  1. Ring theoretic aspects of weak Hopf actions, Preprint MPIM2009-30, Max-Planck Institut für Mathematik, Bonn 2009
  2. Idempotent submodules, preprint CMUP 2006-38
  3. Separable Algebras, lecture notes of a mini-course given in Izmir.
  4. Algebra, lecture notes in portuguese of a course given for Computer Science students during the academic years 2002-2003, 2003-2004, 2004-2005.

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. A painter makes patterns with shapes and colours, a poet with words. A painting may embody any ‘idea’, but the idea is usually commonplace and unimportant. […] A mathematician, on the other hand, has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words ("A Mathematician's Apology").