On Generalizations of Commutativity |
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Authors: | Yang Lee |
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Institution: | 1. Department of Mathematics Education , Pusan National University , Pusan , South Korea ylee@pusan.ac.kr |
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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. |
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Keywords: | Generalization of commutativity Identity-symmetric ring Right duo ring Right near-commutative ring Skew-trivial extension |
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