On graded rings with homogeneous derivations

• Yassine Ait Mohamed ^[1]
  1. [1] Sidi Mohamed Ben Abdellah University

     Sidi Mohamed Ben Abdellah University

     Fes-Medina, Marruecos

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 55-69
• Idioma: inglés
• DOI: 10.33044/revuma.4934
• Enlaces
  • Texto completo
• Resumen

  • We establish results related to homogeneous derivations, a concept introduced by Kanunnikov (2018). First, we prove the existence of a non-trivial family of derivations that are not homogeneous on graded rings. Furthermore, based on homogeneous derivations, we extend certain existing significant results in the context of prime (resp. semiprime) rings to gr-prime (resp. gr-semiprime) rings, such as Posner's and Herstein's theorems.

• Referencias bibliográficas
  • M. Ashraf and N. ur Rehman, On derivation and commutativity in prime rings, East-West J. Math. 3 no. 1 (2001), 87–91. MR Zbl
  • H. E. Bell and W. S. Martindale, III, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 no. 1 (1987), 92–101. DOI MR Zbl
  • M. Breˇsar, Commuting maps: a survey, Taiwanese J. Math. 8 no. 3 (2004), 361–397. DOI MR Zbl
  • M. N. Daif, Commutativity results for semiprime rings with derivations, Internat. J. Math. Math. Sci. 21 no. 3 (1998), 471–474. DOI MR Zbl
  • I. N. Herstein, A note on derivations. II, Canad. Math. Bull. 22 no. 4 (1979), 509–511. DOI MR Zbl
  • A. L. Kanunnikov, Graded quotient rings, J. Math. Sci. (N.Y.) 233 no. 1 (2018), 50–94. DOI MR Zbl
  • I. Kola´rˇ, P. W. Michor, and J. Slovak´ , Natural operations in differential geometry, Springer, Berlin, 1993. DOI MR Zbl
  • J. Lambek, Lectures on rings and modules, Blaisdell, London, 1966. MR Zbl
  • C. Nast ˘ asescu ˘ and F. Van Oystaeyen, Methods of graded rings, Lecture Notes in Mathematics 1836, Springer, Berlin, 2004. DOI MR Zbl
  • E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100. DOI MR Zbl