In this paper, using generalized partial skew versions of Armendariz rings, we study the transfer of left (right) zip property between a ring R and partial skew generalized power series rings

Trinion and Quaternion numbers are one of the hypercomplex which is an extensions complex number. From numbers, a bimodule can be formed ordered pair Quaternion. Furthermore, number, their into Formal Triangle Matrix. The Matrix better known as Upper Since number rings, then called Triangular Ring. purpose this study to construct Armendariz Ring using obtained results will show that Rings -Skew...

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...

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto powerseries rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of...

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...

Recommended by Francois Goichot In this article, we study the relationship between left right zip property of R and skew polynomial extension over R, using the skew versions of Armendariz rings.

 Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...

A ring R is called a right Ikeda-Nakayama (for short IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the left annihilators, that is, if (I ∩ J) = (I) + (J) for all right ideals I and J of R. R is called Armendariz ring if whenever polynomials f (x) = a0 + a1x + ··· + amx, g(x) = b0 + b1x + ··· + bnx ∈ R[x] satisfy f (x)g(x) = 0, then aibj = 0 for each ...