Extensions of McCoy Rings Relative to a Monoid

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 ringαUT_n(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.