Several Studies Of Weak M-McCoy Rings

The current study conducted an extended research based on M-McCoy rings.The first part introduced the concept of M-nil-McCoy rings, discuss the relationship between M-nil-McCoy rings and other rings, and the following results were obtained:1. let M is a u.p.-monoid, if the ring R is a NI ring, then R is a M-nil-McCoy ring,2 let M is a monoid, then Un(R),Ln(R) (n≥2) are M-nil-McCoy rings, 3. let M is a monoid, if the ring R is a M-McCoy ring, then R is a M-nil-McCoy ring.The second part introduced the concept of weak quasi McCoy rings relative to a monoid, get M-weak quasi McCoy rings is real generaliza-tion of M-quasi McCoy rings and weak M-quasi Armendariz rings, and the following results were obtained:1. if M is a commutative and can-cellative monoid containing an infinite submonoid, R is a commutative M-weak quasi McCoy ring, then Mn(R) is a M-weak quasi McCoy ring, 2. if n≥ 2, then Tn(R) is a M-weak quasi McCoy ring,3. if M is a u.p.-monoid, R is a NI ring, then R is a M-weak quasi McCoy ring.