相对于幺半群的McCoy环的扩张

时间:2023-04-26 21:26:57 数理化学论文 我要投稿
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相对于幺半群的McCoy环的扩张

For a monoid M, we introduce M-McCoy rings, which are generalization of McCoy rings, and we investigate their properties. Every M-Armendariz ring is M-McCoy for any monoid M. We show that R is an M-McCoy ring if and only if an n × n upper triangular matrix ring aUTn (R) over R is an M-McCoy ring for any monoid M. It is proved that if R is McCoy and R[x] is M-McCoy, then RIM] is McCoy for any monoid M. Moreover, we prove that if R is M-McCoy, then RIM] and R[x] are M-McCoy for a commutative and cancellative monoid M that contains an infinite cyclic submonoid.

作 者: 杨世洲 宋雪梅 YANG Shi Zhou SONG Xue Me   作者单位: 杨世洲,YANG Shi Zhou(College of Mathematics and Information Science, Northwest Normal University, Gansu 730070, China)

宋雪梅,SONG Xue Me(Department of Mathematics, Lanzhou City University, Gansu 730070, China) 

刊 名: 数学研究与评论  ISTIC PKU 英文刊名: JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION  年,卷(期): 2008 28(3)  分类号: O153.3  关键词: monoid   unique product monoid   McCoy ring   M-McCoy ring   upper triangularmatrix ring  

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