Webpage of Christian Lomp
I am a lecturer (Professor Auxiliar) at the Department of Mathematics of the Faculty of Science of the University of Porto in Porto, Portugal. I am also a member of the editorial board of the International Electronic Journal of Algebra and of the Mathematical Proceedings of the Royal Irish Academy. My research interst lies in Ring and module theory, Hopf algebras and their actions on rings, Coalgebras and their relation to module theory and Algebraic Coding theory. You can find a list of publication on arXiv or AMS. I supervised 6 PhD and 8 Master students (see also Genealogy).
Teaching
Current Courses for which I am currently responsible at the University of Porto (2018/2019)
Past Courses for which I was responsible at the University of Porto.
- M558 Quantum groups, PhD Math.
- M442 Rings and Modules, MSc Math.
- M4029 Commutative Algebra, MSc Math.
- M4081 Algebraic Coding Theory, MSc Math.
- M342 Computer Algebra, BSc Math.
- M341 Galois Theory, BSc 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
- 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)
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 Karacuha, ”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
- Manuel Martins, “Rational equivalence of the quantum plane”, Program “Novos Talentos em Matemática”, Fundação Calouste Gulbenkian 2013/2014
- Artur Amorim, “Characterisation of nilpotent Lie algebras”, Program “Novos Talentos em Matemática”, Fundação Calouste Gulbenkian 2010/2011
- Sérgio Dias, “Van der Waerden numbers and Ramsey theory”, Program “Novos Talentos em Matemática”, Fundação Calouste Gulbenkian 2007/2008
- João Pedro Cunha, high-school student of the program SigMa temático, 2006/2007
- Jorge Victoria, “Plano quântico e o seus simetrias”, research initiation program “Bolsas de iniciação científica”, 2004/2005
- Bruno Jesus “Códigos da convolução”, projecto de Mestade em Engenharia de Matemática, 2005
- Lara Lacerda, “Neural networks”, Program “Novos Talentos em Matemática”, Fundação Calouste Gulbenkian 2003/2004
Postdoctoral Researcher
- Zahra Nazemian, Yazd (Iran), December 2016 - March 2017
- Tuğba Güroğlu, Celal Bayar University (Turkey), 30.March - 27. June 2012
- Engin Büyükaşık, Izimir Institute of Technology (Turkey), 16. September 2007 - 16. A$
- Alveri Sant’Ana, Universidade Federal do Rio Grande do Sul (Brazil), 1. March 2006 -$
- Vigínia Rodrigues, Universidade Federal de Santa Clara (Brazil), 9. September 200$
Brief CV
- 2011 Agregação (Habilitation), Universidade do Porto
- 2002-now 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
- 1995 Vordiplom Informatik, Fernuni-Hagen, grade: “sehr gut”
- 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
ORCID
MathSciNet ID: 641518/ ZMATH / Scopus Author ID: 14630520600/ Orcid ID: 0000-0003-2475-3448/ ResearcherID: D-1361-2010/ Research Gate
An up-to-date list can be found either on arXiv or on
ORCID.
Papers
- A note on simple modules over quasi-local rings (with P.Carvalho and P.F.Smith), Int. Elect. J. Algebra 24 (2018) 91-106
- Panov's theorem for weak Hopf algebras (with A.Sant'Ana and R.Leite dos Santos), Contemp. Math. AMS (in press)
- Differential smoothness of skew polynomial rings (with Tomasz Brzeziński), Journal of Pure and Applied Algebra 222(9) (2018) 2413-2426, arXiv:1609.04055
- A counterexample for a problem on quasi Baer modules Taiwanese J. Math. 21 (2017), no. 6, 1277–128, arXiv:1605.02297
- Ring theoretical properties of affine cellular algebras (with Paula A. A. B. Carvalho, Steffen Koenig and Armin Shalile), Journal of Algebra (2017), [[https://arxiv.org/abs/1609.01771|arXiv:1609.01771]]
- A note on a paper by Cuadra, Etingof and Walton (with Deividi Pansera), Communications in Algebra (2017), [[http://arxiv.org/abs/1506.07766|arXiv:1506.07766
- A note on semicentral idempotents (with Jerzy Matczuk), Communications in Algebra 45 no. 6 (2017) 2735 - 2737, [[https://arxiv.org/abs/1605.02360|arXiv:1605.02360]]
- On Topological Lattices and their Applications to Module Theory (with Jawad Abuhlail), J. Algebra Appl. 15 (2016), no. 3, 1650046, 21 pp. [[http://arxiv.org/abs/1305.4578 |arXiv:1305.4578 ]]
- Injective hulls of simple modules over differential operator rings (with Paula Carvalho and Can Hatipoglu), Communications in Algebra 43 (2015), 4221-4230 [[http://arxiv.org/abs/1211.2592|arXiv:1211.2592]]
- A note on dimension modules (with Edmund Puczylowski), Communications in Algebra 43 (2015) 2267–2271
- Endomorphism rings of modules over prime rings (with M.Baziar), Taiwanese Journal of Mathematics 19 (2015), 953-962
- Integral Calculus on Quantum Exterior Algebras (with Serkan Karaçuha) Int. J. Geom. Methods Mod. Phys. 11, 1450026 (2014), DOI: 10.1142/S0219887814500261 [[http://arxiv.org/abs/1302.5216 |arXiv:1302.5216 ]]
- On the notion of strong irreducibility and its dual (with J.Abuhlail) Journal of Algebra and its Applications 12,1350012 (2013), [[http://arxiv.org/abs/1207.4227|arXiv:1207.4227]].
- Injective hulls of simple modules over finite dimensional nilpotent complex Lie superalgebras (with C.Hatipoglu), Journal of Algebra, Volume 361 (2012), 79-91
- Quantum Groupoids acting on semiprime algebras (with I.Borges) Advances in Mathematical Physics (2011) 9pp
- Fleury's spanning dimension and chain conditions on non-essential elements in modular lattices (with A.C.Ozcan) Colloquium Mathematicum 124 (2011), 133-144
- Irreducible Actions and Compressible Modules (with I.Borges), Journal of Algebra and its Applications 10(1), 101-117 (2011), [[http://arxiv.org/abs/1003.4108|arXiv:1003.4108]]
- Injective Modules over Down-Up algebras (with Paula A.A.B. Carvalho and Dilek Pusat-Yilmaz), Glasgow Mathematical Journal 52A 53-59 (2010)
- Non-commutative integral forms and twisted multi-derivations (with T.Brzezinski and L.El Kaoutit), Journal of Noncommutative Geometry 4(2) 281-312 (2010)
- When δ-semiperfect rings are semiperfect. (with E.Büyükasik), Turkish Journal of Mathematics 34, 317 – 324 (2010).
- Rings whose modules are weakly supplemented are perfect. Applications to certain ring extensions. (with E.Büyükasik), Mathematica Scandinavia 105 (2009), 25-30
- All hereditary torsion theories are differential. (with J. van den Berg), Journal of pure and applied Algebra 213 (2009), 476-478
- 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)
- Regular and biregular module algebras. Arabian Journal for Science and Engineering 33 (2c), 351-364 (2008)
- Duality for partial group actions International Electronic Journal of Algebra 4 53-62 (2008)
- On a recent generalization of semiperfect rings. (with E.Büyükasik) Bulletin of the Australian Mathematical Society 78(2), 317-325 (2008)
- Covering coalgebras and dual non-singularity (with V.Rodrigues), Applied Categorical Structures 16(2008), 195-211
- Chain and Distributive Coalgebras (with A.Sant'Ana), Journal of Pure and Applied Algebra, 211(3), 581-595 (2007)
- A note on extending Hopf algebra actions to rings of quotients Beiträge zur Algebra und Geometrie 47(1), 137-146 (2006)
- An example of an indecomposable module without non-zero hollow factor modules Turkish Journal Math 31(4)(2006), 1-5
- τ-complemented and τ-supplemented modules (with K.Al-Takhman and R.Wisbauer), Algebra and Disrete Mathematics 3 (2006) 1-15
- A central closure construction for certain extensions. Applications to Hopf actions Journal of Pure and applied Algebra, 198 (1-3), 297-316 (2005)
- Prime elements in partially ordered groupoids applied to modules and Hopf algebra actions. Journal of Algebra and its Applications, 4(1), 77-98 (2005)
- Integrals in Hopf algebras over rings Communications in Algebra, 32(12), 4687-4711 (2004)
- When is a smash product semiprime? A partial answer Journal of Algebra 275(1), 339-355 (2004)
- 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)
- A remark on a theorem of Y.Kurata” Hokkaido Journal of Mathematics 30 (3), 645-648 (2001)
- A note on prime modules (with A.J.Pena P.), Divulgaciones Mathematica 8(1), 31-42 (2000)
- 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)
- Semilocal modules and rings Communications in Algebra 27(4), 1921-1935 (1999)
- Modules whose small submodules have Krull dimension Journal of Pure and applied Algebra 133(1-2), 197-202 (1998)
Survey Papers in conference proceedingsa
- (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
- (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)
- (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
- 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
Unpublished Notes and Reports