Publications of Piotr Grzeszczuk

Published papers:

  1. Classical radicals of invariants of algebraic skew derivations,  Algebra Colloquium,  29(1) (2022), 53-66. https://doi.org/10.1142/S1005386722000050 (with Jeffrey Bergen)
  2. On the generic family of Cayley graphs of a finite group, J. Combinatorial Theory Ser A,  184, (2021) , 40 pp. ,  https://doi.org/10.1016/j.jcta.2021.105495, (with Czesław Bagiński)
  3. Locally nilpotent skew extensions of rings, J. Pure Appl. Algebra, 224 (2020), 106360, https://doi.org/10.1016/j.jpaa.2020.106360   arXiv
  4. On the semiprimitivity of free skew extensions of rings, J. Pure Appl. Algebra,  (2020),   https://doi.org./10.1016/j.jpaa.2020.106307 (with Jeffrey Bergen) arXiv
  5. Jacobson radicals of invariants under Hopf algebra actions, J. Algebra and its Applications, 17(7) (2018), 1850132, 10 pp. (with Jeffrey Bergen)
  6. Locally nilpotent skew derivations with central invariants, J. Algebra, 483 (2017), 71-82. (with Jeffrey Bergen)
  7. Skew derivations with algebraic invariants of bounded degree,  J. Algebra, 447 (2016), 455-467. (with Jeffrey Bergen) DOI
  8. Invariants of domains with finite GK dimension, Monatshefte für Mathematik, 179,  (2016),  191-199. (with Jeffrey Bergen) DOI
  9. Gelfand-Kirillov dimension of algebras with locally nilpotent derivations, Israel J. Math. 206 (2015), no. 1, 313-325. (with Jeffrey Bergen) DOI
  10. GK dimension and locally nilpotent skew derivations, Glasgow Mathematical Journal, 57(3)  (2015), 555-567.  (with Jeffrey Bergen) DOI
  11. On the Jacobson radical of constants of derivations,  J. Algebra 401 (2014), 62-75. DOI
  12. On irreducible modules over q-skew polynomial rings and smash products, Proc. Amer. Math. Soc. 142 (2014), no. 1, 59-69. PDF  DOI 
  13. Skew derivations and the nil and prime radicals, Colloquium Mathematicum, 128 (2012), no. 2, 229-236. (with Jeffrey Bergen) PDF
  14. Goldie dimension of constants of locally nilpotent skew derivations, J. Algebra Appl. 11 (2012), no. 6, 1250105, 12 pp. (with Jeffrey Bergen) DOI   PDF
  15. Jacobson radicals of ring extensions,  J. Pure Appl. Algebra 216 (2012), no. 12, 2601-2607. (with Jeffrey Bergen) DOI  PDF
  16. Skew power series rings of derivation type, J. Algebra Appl. 10 (2011), no. 6, 1383-1399. (with Jeffrey Bergen) PDF
  17. On rings with locally nilpotent skew derivations,  Comm. Algebra 39 (2011), no. 10, 3698-3708. (with Jeffrey Bergen) PDF
  18. Actions of Lie superalgebras on semiprime algebras with central invariants,  Glasgow Mathematical Journal, 52 (2010), no. A, 93-102. (with Małgorzata Hryniewicka) PDF
  19. Actions of Lie superalgebras on reduced rings,  Algebr. Represent. Theory 11 (2008), no. 3, 251-273. (with Jeffrey Bergen and Małgorzata Hryniewicka) PDF
  20. Finite block theory and Hopf algebra actions,  Algebr. Represent. Theory 11 (2008), no. 1, 1-23. (with Jeffrey Bergen)
  21. Actions of pointed Hopf algebras with reduced PI invariants, Proc. Amer. Math. Soc. 135 (2007), no. 8, 2381-2389. (with Małgorzata Hryniewicka)
  22. Smash products satisfying a polynomial identity,  Comm. Algebra 33 (2005), no. 1, 221-233. (with Jeffrey Bergen)
  23. Polynomial identities of algebras with actions of pointed Hopf algebras,  J. Algebra 278 (2004), no. 2, 684-703. (with Małgorzata Hryniewicka)
  24. Invariants of semisimple Lie algebras acting on associative algebras, Proc. Amer. Math. Soc. 131 (2003), no. 3, 709-717.
  25. The prime radical of constants of algebraic q-skew derivations, Comm. Algebra 30 (2002), no. 11, 5331-5343. (with Jerzy Matczuk)
  26. Simple Jordan color algebras arising from associative graded algebras, J. Algebra 246 (2001), no. 2, 915-950. (with Jeffrey Bergen)
  27. Artinian property of constants of algebraic q-skew  derivations,  Israel J. Math. 121 (2001), 265-284. (with Andre Leroy and Jerzy Matczuk)
  28. Skew derivations whose invariants satisfy a polynomial identity,  J. Algebra 228 (2000), no. 2, 710-737. (with Jeffrey Bergen)
  29. Invariants of Lie color algebras acting on graded algebras,  Colloq. Math. 83 (2000), no. 1, 107-124. (with Jeffrey Bergen)
  30. Skew derivations with central invariants,  J. London Math. Soc. (2) 59 (1999), no. 1, 87-99. (with Jeffrey Bergen)
  31. Invariants of  Uq(sl2) and q-skew derivations, Ring theory (Miskolc, 1996). J. Pure Appl. Algebra 133 (1998), no. 1-2, 27-38. (with Jeffrey Bergen)
  32. On finiteness conditions of modular lattices,  Comm. Algebra 26 (1998), no. 9, 2949-2957. (with Edmund R. Puczylowski)
  33. Invariants of skew derivations,  Proc. Amer. Math. Soc. 125 (1997), no. 12, 3481-3488. (with Jeffrey Bergen)
  34. Invariants of Lie superalgebras acting on associative algebras,  Israel J. Math. 94 (1996), 403-428. (with Jeffrey Bergen)
  35. Gradings, derivations, and automorphisms of nearly associative algebras,  J. Algebra 179 (1996), no. 3, 732-750. (with Jeffrey Bergen)
  36. A radical of lattices and its applications to rings and modules,  Contributions to general algebra, 9 (Linz, 1994), 203-212, Hölder-Pichler-Tempsky, Vienna, 1995. (with Edmund R. Puczylowski)
  37. On derivations with powers vanishing on one-sided ideals, Chinese J. Math. 23 (1995), no. 4, 311-317.
  38. Actions of Lie algebras on rings without nilpotent elements, Algebra Colloq. 2 (1995), no. 2, 105-116. (with Kostia Beidar)
  39. On constants of algebraic derivations and fixed points of algebraic automorphisms,  J. Algebra 171 (1995), no. 3, 826-844.
  40. Engel-type theorems for Lie color algebras,  Rings, extensions, and cohomology (Evanston, IL, 1993), 31-33, Lecture Notes in Pure and Appl. Math., 159, Dekker, New York, 1994. (with Jeffrey Bergen)
  41. Goldie conditions for constants of algebraic derivations of semiprime algebras, Israel J. Math. 83 (1993), no. 3, 329-342. (with Jerzy Matczuk)
  42. Constants of algebraic derivations, Comm. Algebra 21 (1993), no. 6, 1857-1868.
  43. The Goldie dimension of some extensions of modular lattices, Proceedings of the International Conference on Algebra, Part 3 (Novosibirsk, 1989), 111-119, Contemp. Math., 131, Part 3, Amer. Math. Soc., Providence, RI, 1992.
  44. On nilpotent derivations of semiprime rings,  J. Algebra 149 (1992), no. 2, 313-321.
  45. The Gabriel dimension is not autodual,  Comm. Algebra 18 (1990), no. 8, 2587-2594.
  46. Relations between some dimensions of modular lattices,  Comm. Algebra 17 (1989), no. 7, 1723-1737. (with Jan Okninski and Edmund R. Puczylowski)
  47. Gabriel and Krull dimensions of modules over rings graded by finite groups,  Proc. Amer. Math. Soc. 105 (1989), no. 1, 17-24. (with Edmund R. Puczylowski)
  48. Dual Gabriel dimension of modules with derivations, Comm. Algebra 16 (1988), no. 8, 1689-1699.
  49. Goldie dimension of differential operator rings, Comm. Algebra 16 (1988), no. 4, 689-701.
  50. On derivations of finite index chain conditions, dimensions and radicals,  Israel J. Math. 58 (1987), no. 1, 54-66.
  51. Goldie dimension and chain conditions for modular lattices with finite group actions, Canad. Math. Bull. 29 (1986), no. 3, 274-280. (with Edmund R. Puczylowski)
  52. On G-systems and G-graded rings, Proc. Amer. Math. Soc. 95 (1985), no. 3, 348-352.
  53. On infinite Goldie dimension of modular lattices and modules,  J. Pure Appl. Algebra 35 (1985), no. 2, 151-155. (with Edmund R. Puczylowski)
  54. On Goldie and dual Goldie dimensions,  J. Pure Appl. Algebra 31 (1984), no. 1-3, 47-54. (with Edmund R. Puczylowski)
    55.