相对于幺半群的McCoy环  

McCoy rings relative to a monoid

作　　者：宋雪梅[1] 杨世洲[1] 

机构地区：[1]西北师范大学数学与信息科学学院

出　　处：《兰州大学学报（自然科学版）》2007年第6期85-91,共7页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金(10171082);甘肃省自然科学基金(3ZS061-A25-015);甘肃省教育厅科研基金(0601-21)资助项目.

摘　　要：对于幺半群M,引入了M-McCoy环并研究了它的性质,证明了对于任意的u.p.-幺半群M,可逆环都是M-McCoy环.得到了对于幺半群M,u.p.-幺半群N,若R是交换的M-McCoy环,则R是M×N-McCoy环.证明了M-McCoy环的直积是M-McCoy环及在一定条件下M-McCoy环的子环是M- McCoy环.同时也证明有限生成的阿贝尔群G是无挠群当且仅当存在一个环R,使得R是G-McCoy环.For a monoid M, M-McCoy rings is introduced and their properties are investigated. Every reversible ring is M-McCoy for any unique product monoid M. It is showed that if R is a commutative and M-McCoy ring, then R is a M x N-McCoy ring, where M is a commutative monoid and N is a unique product monoid, and that the direct products of M-McCoy rings is M-McCoy and under certain conditions the subrings of M-McCoy rings are M-McCoy rings. Meanwhile, It is proved that a finitely generated Abelian group G is torsion free if and only if there exists a ring R such that R is G-McCoy.

关 键 词：幺半群 u.P.-幺半群 McCoy环 M—McCoy环 直积 

分 类 号：O153.3[理学—数学]