SYMMETRIC PROPERTY OF RINGS WITH RESPECT TO THE JACOBSON RADICAL

ÇALCI T., HALICIOĞLU S., Harmanci A.

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, vol.34, no.1, pp.43-54, 2019 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.4134/ckms.c170473
  • Journal Name: COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.43-54
  • Keywords: symmetric ring, J-symmetric ring, ring extension, MODULES
  • Ankara University Affiliated: Yes

Abstract

Let R be a ring with identity and J(R) denote the Jacobson radical of R, i.e., the intersection of all maximal left ideals of R. A ring R is called J-symmetric if for any a, b, c is an element of R, abc = 0 implies bac is an element of J(R). We prove that some results of symmetric rings can be extended to the J-symmetric rings for this general setting. We give many characterizations of such rings. We show that the class of J-symmetric rings lies strictly between the class of symmetric rings and the class of directly finite rings.