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- Title
(g,e)-Symmetric Rings.
- Authors
Meng, Fanyun; Wei, Junchao
- Abstract
Let R be a ring and e , g in E (R) , the set of idempotents of R. Then R is called (g , e) -symmetric if a b c = 0 implies g a c b e = 0 for any a , b , c ∈ R. Clearly, R is an e -symmetric ring if and only if R is a (1 , e) -symmetric ring; in particular, R is a symmetric ring if and only if R is a (1 , 1) -symmetric ring. We show that e ∈ E (R) is left semicentral if and only if R is a (1 − e , e) -symmetric ring; in particular, R is an Abel ring if and only if R is a (1 − e , e) -symmetric ring for each e ∈ E (R). We also show that R is (g , e) -symmetric if and only if g e ∈ E (R) , g e R g e is symmetric, and g x y e = g x e y e = g x g y e for any x , y ∈ R. Using e -symmetric rings, we construct some new classes of rings.
- Subjects
IDEMPOTENTS
- Publication
Algebra Colloquium, 2024, Vol 31, Issue 2, p263
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386724000208