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相對(duì)于幺半群的McCoy環(huán)的擴(kuò)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(shù)學(xué)研究與評(píng)論 ISTIC PKU 英文刊名: JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION 年,卷(期): 2008 28(3) 分類號(hào): O153.3 關(guān)鍵詞: monoid unique product monoid McCoy ring M-McCoy ring upper triangularmatrix ring【相對(duì)于幺半群的McCoy環(huán)的擴(kuò)張】相關(guān)文章:
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