Quotient rings satisfying some identities

• Autores: Mohammadi El Hamdaoui, Abdelkarim Boua
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 25, Nº. 3, 2023, págs. 455-465
• Idioma: inglés
• DOI: 10.56754/0719-0646.2503.455
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen Este artículo investiga la conmutatividad del anillo cociente R/P, donde R es un anillo asociativo con un ideal primo P, y la posibilidad de formas de derivaciones que satisfacen ciertas identidades algebraicas en R. Entregamos algunos resultados para derivaciones de anillos primos que preservan la conmutatividad fuerte.

  • English

    Abstract This paper investigates the commutativity of the quotient ring R/P, where R is an associative ring with a prime ideal P, and the possibility of forms of derivations satisfying certain algebraic identities on R. We provide some results for strong commutativity-preserving derivations of prime rings.

• Referencias bibliográficas
  • Ali, A.,Yasen, M.,Anwar, M.. (2006). Strong commutativity preserving mappings on semiprime rings. Bull. Korean Math. Soc.. 43. 711
  • Almahdi, F. A. A.,Mamouni, A.,Tamekkante, M.. (2020). A generalization of Posner’s Theorem on derivations in rings. Indian J. Pure Appl. Math.....
  • Beidar, K. I.,Martindale III, W. S.,Mikhalev, A. V.. (1996). Rings with generalized identities. Marcel Dekker, Inc.. New York, USA.
  • Bell, H. E.,Daif, M. N.. (1994). On commutativity and strong commutativity-preserving maps. Canad. Math. Bull.. 37. 443
  • Bell, H. E.,Mason, G.. (1992). On derivations in near-rings and rings. Math. J. Okayama Univ.. 34. 135
  • Brešar, M.. (1990). Semiderivations of prime rings. Proc. Amer. Math. Soc.. 108. 859
  • Brešar, M.. (1991). On the distance of the composition of two derivations to the generalized derivations. Glasgow Math. J.. 33. 89-93
  • Brešar, M.. (1993). Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings. Trans. Amer. Math. Soc.....
  • Brešar, M.,Miers, C. R.. (1994). Strong commutativity preserving maps of semiprime rings. Canad. Math. Bull.. 37. 457
  • Deng, Q.,Ashraf, M.. (1996). On strong commutativity preserving mappings. Results Math.. 30. 259
  • Lee, T.-K.,Wong, T.-L.. (2012). Nonadditive strong commutativity preserving maps. Comm. Algebra. 40. 2213
  • Lin, J.-S.,Liu, C.-K.. (2008). Strong commutativity preserving maps on Lie ideals. Linear Algebra Appl.. 428. 1601
  • Lin, J.-S.,Liu, C.-K.. (2010). Strong commutativity preserving maps in prime rings with involution. Linear Algebra Appl.. 432. 14-23
  • Liu, C.-K.. (2012). Strong commutativity preserving generalized derivations on right ideals. Monatsh. Math.. 166. 453
  • Liu, C.-K.,Liau, P.-K.. (2011). Strong commutativity preserving generalized derivations on Lie ideals. Linear Multilinear Algebra. 59. 905
  • Ma, J.,Xu, X. W.,Niu, F. W.. (2008). Strong commutativity-preserving generalized derivations on semiprime rings. Acta Math. Sin. (Engl. Ser.)....
  • Posner, E. C.. (1957). Derivations in prime rings. Proc. Amer. Math. Soc.. 8. 1093
  • Samman, M. S.. (2005). On strong commutativity-preserving maps. Int. J. Math. Math. Sci.. 2005. 917
  • Šemrl, P.. (2008). Commutativity preserving maps. Linear Algebra Appl.. 429. 1051