Abstract:

M-quasi-McCoy rings are introduced, and their properties are investigated. It is shown that, for any unique product monoid M, every reversible ring is M-quasi-McCoy. If M is a commutative and cancellative monoid containing an infinite cyclic submonoid, N is a u.p. monoid and R is a commutative M-quasiMcCoy ring, then R［N］ is M-quasi-McCoy and R is M×N-quasi-McCoy. For a monoid M, R is M-quasi-McCoy ring if and only if upper triangular matrix ring Tn(R)  is M-quasi-McCoy ring and direct product ∏i∈IRi is M-quasi-McCoy ring if and only if each ring Ri(i∈I)  is M-quasi-McCoy ring.

Key words: monoid; unique product monoid; M-quasi-McCoy ring; M-quasi-Armendariz ring; upper triangular matrix ring; direct product