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- W2044809100 abstract "This note is concerned with generalizations of commutativity. We introduce identity-symmetric and right near-commutative, and study basic structures of rings with such ring properties. It is shown that if R is an identity-symmetric ring, then the set of all nilpotent elements forms a commutative subring of R. Moreover, identity-symmetric regular rings are proved to be commutative. The near-commutativity is shown to be not left-right symmetric, and we study some conditions under which the near-commutativity is left-right symmetric. We also examine the near-commutativity of skew-trivial extensions, which has a role in this note." @default.
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- W2044809100 date "2015-01-28" @default.
- W2044809100 modified "2023-09-23" @default.
- W2044809100 title "On Generalizations of Commutativity" @default.
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- W2044809100 doi "https://doi.org/10.1080/00927872.2013.876035" @default.
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