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 o...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.展开更多
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）.
文摘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.
