On Weak Armendariz Rings |
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| Authors: | Zhongkui Liu Renyu Zhao |
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| Institution: | 1. Department of Mathematics , Northwest Normal University , Lanzhou, China liuzk@nwu.edu.cn;3. Department of Mathematics , Northwest Normal University , Lanzhou, China |
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| Abstract: | We introduce weak Armendariz rings which are a generalization of semicommutative rings and Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak Armendariz if and only if for any n, the n-by-n upper triangular matrix ring T n (R) is weak Armendariz. If R is semicommutative, then it is proven that the polynomial ring Rx] over R and the ring Rx]/(x n ), where (x n ) is the ideal generated by x n and n is a positive integer, are weak Armendariz. |
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| Keywords: | Armendariz ring Semicommutative ring Weak Armendariz ring |
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