[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c210240

COMMUTATIVITY CRITERIA OF PRIME RINGS INVOLVING TWO ENDOMORPHISMS

Dakir, Souad (Department of Mathematics Faculty of Science University Moulay Ismail Meknes)
Mamouni, Abdellah (Department of Mathematics Faculty of Science University Moulay Ismail Meknes)
Tamekkante, Mohammed (Department of Mathematics Faculty of Science University Moulay Ismail Meknes)

Publication Information

Communications of the Korean Mathematical Society / v.37, no.3, 2022 , pp. 659-667 More about this Journal

Abstract

This paper treats the commutativity of prime rings with involution over which elements satisfy some specific identities involving endomorphisms. The obtained results cover some well-known results. We show, by given examples, that the imposed hypotheses are necessary.

Keywords

Prime ring; involution; commutativity; endomorphisms of rings;

Citations & Related Records

Reference

1	M. Bresar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), no. 2, 385-394. https://doi.org/10.1006/jabr.1993.1080 DOI
2	M. Bresar, W. S. Martindale, III, and C. R. Miers, Centralizing maps in prime rings with involution, J. Algebra 161 (1993), no. 2, 342-357. https://doi.org/10.1006/jabr.1993.1223 DOI
3	Q. Deng and H. E. Bell, On derivations and commutativity in semiprime rings, Comm. Algebra 23 (1995), no. 10, 3705-3713. https://doi.org/10.1080/00927879508825427 DOI
4	A. Mamouni, L. Oukhtite, and B. Nejjar, On -semiderivations and -generalized semiderivations, J. Algebra Appl. 16 (2017), no. 4, 1750075, 8 pp. https://doi.org/10.1142/S021949881750075X DOI
5	H. El Mir, A. Mamouni, and L. Oukhtite, Special mappings with central values on prime rings, Algebra Colloq. 27 (2020), no. 3, 405-414. https://doi.org/10.1142/S1005386720000334 DOI
6	B. Nejjar, A. Kacha, A. Mamouni, and L. Oukhtite, Commutativity theorems in rings with involution, Comm. Algebra 45 (2017), no. 2, 698-708. https://doi.org/10.1080/00927872.2016.1172629 DOI
7	E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100. https://doi.org/10.2307/2032686 DOI
8	J. H. Mayne, Centralizing automorphisms of prime rings, Canad. Math. Bull. 19 (1976), no. 1, 113-115. https://doi.org/10.4153/CMB-1976-017-1 DOI