相對于幺半群的McCoy環的擴張

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： 楊世洲 宋雪梅 YANG Shi Zhou SONG Xue Me   作者單位： 楊世洲,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： 數學研究與評論  ISTIC PKU 英文刊名： JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION  年，卷(期)： 2008 28(3)  分類號： O153.3  關鍵詞： monoid   unique product monoid   McCoy ring   M-McCoy ring   upper triangularmatrix ring  

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