Quasi-Armendariz Rings Relative to a Monoid |
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Authors: | Liu Zhongkui Zhang Wenhui |
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Institution: | 1. Department of Mathematics , Northwest Normal University , Lanzhou, Gansu, China liuzk@nwnu.edu.cn;3. Department of Mathematics , Northwest Normal University , Lanzhou, Gansu, China |
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Abstract: | A ring R is called an M-quasi-Armendariz ring (a quasi-Armendariz ring relative to a monoid M) if whenever elements α = a 1 g 1 + a 2 g 2 + ··· + a n g n , β = b 1 h 1 + b 2 h 2 + ··· + b m h m ? RM] satisfy α RM]β = 0, then a i Rb j = 0 for each i, j. After discussing some basic properties of M-quasi-Armendariz rings, we consider the influence of transformation of the monoid M and the ring R on this property. Particularly, we give some sufficient conditions for the monoids M, N, and the ring R under which R is M × N-quasi-Armendariz if and only if R is M-quasi-Armendariz and N-quasi-Armendariz. |
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Keywords: | Armendariz ring Left APP-ring M-quasi-Armendariz ring |
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