SYMMETRIC PROPERTY OF RINGS WITH RESPECT TO THE JACOBSON RADICAL
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, cilt.34, sa.1, ss.43-54, 2019 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 34 Sayı: 1
- Basım Tarihi: 2019
- Doi Numarası: 10.4134/ckms.c170473
- Dergi Adı: COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.43-54
- Anahtar Kelimeler: symmetric ring, J-symmetric ring, ring extension, MODULES
- Ankara Üniversitesi Adresli: Evet
Özet
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.