in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.

Abstract The reactions of the N‐heterocyclic carbene‐parent phosphinidene adducts (IMes)PH ( 1 a ) and (IDipp)PH b with one equivalent copper(I) or silver(I) chloride afforded monometallic complexes [{(IMes)PH}MCl] 2 , M=Cu; M=Ag) [{(IDipp)PH}MCl] 3 M=Ag). Single‐crystal X‐ray diffraction analyis provided evidence for higher tendency ligand to form polynuclear structures bridging NHC‐phosphinid...

we introduce the class of “right almost v-rings” which is properly between the classes of right v-rings and right good rings. a ring r is called a right almost v-ring if every simple r-module is almost injective. it is proved that r is a right almost v-ring if and only if for every r-module m, any complement of every simple submodule of m is a direct summand. moreover, r is a right almost v-rin...

We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-rin...

The title compound, [Ru(C7F5O2)2(C10H14)(C21H24N2)]·2CH2Cl2, is formed as an orange crystalline powder by the reaction of RuCl2(p-cymene)(IMes) and AgOCOC6F5 in anhydrous tetra-hydro-furan (IMes = 1,3-dimesityl-2,3-di-hydro-1H-imidazol-2-yl-idene). The asymetric unit consists of two independent [Ru(C6F5COO)2(η(6)-p-cymene)(IMes)] com-plexes and four dichloro-methane solvent mol-ecules. In each ...

A ring $R$ with identity is called ``clean'' if $~$for every element $ain R$, there exist an idempotent $e$ and a unit $u$ in $R$ such that $a=u+e$. Let $C(R)$ denote the center of a ring $R$ and $g(x)$ be a polynomial in $C(R)[x]$. An element $rin R$ is called ``g(x)-clean'' if $r=u+s$ where $g(s)=0$ and $u$ is a unit of $R$ and, $R$ is $g(x)$-clean if every element is $g(x)$-clean. In this pa...

We prove that all trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$ are nil-clean and, up to similarity, there only two $\mathbb{Z}$.

Let R be an Abelian exchange ring. We prove the following results: 1. RZ2 and RS3 are clean rings. 2. If G is a group of prime order p and p is in the Jacobson radical of R, then RG is clean. 3. If identity in R is a sum of two units and G is a locally finite group, then every element in RG is a sum of two units. 4. For any locally finite group G, RG has stable range one. All rings in this note...

in this paper we introduce strongly $left[  v_{2},lambda_{2},m,pright]-$summable double vsequence spaces via orlicz function and examine someproperties of the resulting these spaces. also we give natural relationshipbetween these spaces and $s_{lambda_{2}}-$statistical convergence.