Extensions of McCoy Rings Relative to a Monoid  

作　　者：YANG Shi Zhou SONG Xue Mei 

机构地区：[1]College of Mathematics and Information Science, Northwest Normal University, Gansu 730070, China [2]Department of Mathematics, Lanzhou City University, Gansu 730070, China

出　　处：《Journal of Mathematical Research and Exposition》2008年第3期659-665,共7页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China （No. 10171082）; the Natural Science Foundation of Gansu Province （No. 3ZSA061-A25-015） and the Scientific Research Fund of Gansu Provincial Education Department （Nos. 06021-21; 0410B-09）.

摘　　要：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 αUTn （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 R[M] is McCoy for any monoid M. Moreover, we prove that if R is M-McCoy, then R[M] and R[x] are M-McCoy for a commutative and cancellative monoid M that contains an infinite cyclic submonoid.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 αUTn （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 R[M] is McCoy for any monoid M. Moreover, we prove that if R is M-McCoy, then R[M] and R[x] are M-McCoy for a commutative and cancellative monoid M that contains an infinite cyclic submonoid.

关 键 词：MONOID unique product monoid McCoy ring M-McCoy ring upper triangular matrix ring. 

分 类 号：O153.3[理学—数学]