Reflexivity with maximal ideal axes
2016; Taylor & Francis; Volume: 45; Issue: 10 Linguagem: Inglês
10.1080/00927872.2016.1222398
ISSN1532-4125
AutoresAbdullah M. Abdul-Jabbar, Chenar Abdul Kareem Ahmed, Tai Keun Kwak, Yang Lee,
Tópico(s)Algebraic structures and combinatorial models
ResumoThe reflexive property for ideals was introduced by Mason and has important roles in noncommutative ring theory. We in this note study rings with the reflexivity whose axis is given by maximal ideals (simply, an RM ring) which are a generalization of symmetric rings. It is first shown that the reflexivity of a ring and the RM ring property are independent of each other, noting that both of them are generalizations of ideal-symmetric rings. We connect RM rings with reflexive rings in various situations raised naturally in the procedure. As a generalization of RM rings, we also study the structure of the reflexivity with the maximal ideal axis on idempotents (simply, an RMI ring) and then investigate the structure of minimal non-Abelian RMI rings (with or without identity) up to isomorphism.
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