For a monoid M , we introduce linear M-Armendariz rings, which are generalization of M-Armendariz rings and linear Armendariz rings; and investigate their properties. Every reduced ring is linear M-Armendariz, for any unique product monoid. We show that if M be a monoid and R be a right ore ring with classical right quotient ring Q. Then R is linear M-Armendariz if and only if Q is linear M-Arm...

Let $R$ be a unitary ring with an endomorphism $σ$ and $F∪{0}$ be the free monoid generated by $U={u_1,…,u_t}$ with $0$ added, and $M$ be a factor of $F$ setting certain monomial in $U$ to $0$, enough so that, for some natural number $n$, $M^n=0$. In this paper, we give a sufficient condition for a ring $R$ such that the skew monoid ring $R*M$ is quasi-Armendariz (By Hirano a ring $R$ is called...

The main result of this paper is that for a commutative ring R and finitely generated submonoids M and N of Z2 the monoid rings R [M] and R[N] are isomorphic as R algebras if and only if M and N are isomorphic. In the course of proof we derive various results concerning the structure of rank 2 monoids and isomorphisms between the corresponding monoid rings. 1991 Math. Subj. Class.: 13B25, 20M25...

Following a construction of Stanley we consider toric face rings associated to rational pointed fans. This class of rings is a common generalization of the concepts of Stanley–Reisner and affine monoid algebras. The main goal of this article is to unify parts of the theories of Stanley–Reisnerand affine monoid algebras. We consider (nonpure) shellable fan’s and the Cohen–Macaulay property. More...