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.
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
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.
