We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...

the internal mammary artery (ima) is currently the preferred conduit for myocardial revascularization. however, pre-operative vasospasm and a hypoperfusion state during maximal exercise may limit its use as a bypass graft. the mechanism of spasm has not been clearly defined. since β-adrenoceptor activation plays a major role in vasorelaxation, the present study was carried out to investigate th...

The asymmetric unit of the title compound,  Contains two independent molecules. The Cu atoms are four coordinated in distorted tetrahedral configuration by two atoms from 5,5`-dimethyl-2,2`- bipyridine and two terminal atoms. In the Cuystal structure, inter molecular hydrogen bonds link the molecules. The are  contacts between the methyl groups and the pyridine and five member rings containing ...

In this study, the combination of Phenergan C17H2ON2S, in which two aromatic rings are present, are attached to the rings at carbon position 5 and 13 halogens, and the changes in the asymmetric parameter, the convex constants, and the chemical displacement of the lateral carbon atoms are calculated. It shows that with the change of halogen based on the electrone...

a polynomial   1 2 ( , , , ) n f x x x is called multilinear if it is homogeneous and linear in every one of its variables. in the present paper our objective is to prove the following result: let   r be a prime k-algebra over a commutative ring   k with unity and let 1 2 ( , , , ) n f x x x be a multilinear polynomial over k. suppose that   d is a nonzero derivation on r such that ...

the aim of this paper is to study orders over a valuation ring v with arbitrary rank in acentral simple f-algebra q. the relation between all of the orders is explained with a diagram. it is thenshown that inside bezout order, extremal v-orders are precisely semi-hereditary. in the last section, theeffect of henselization on maximal and semi-hereditary orders is examined.

let $r$ be a commutative ring with identity and $mathbb{a}(r)$ be the set   of ideals of $r$ with non-zero annihilators. in this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $r$, denoted by $mathbb{ag}_p(r)$. it is a (undirected) graph with vertices $mathbb{a}_p(r)=mathbb{a}(r)cap mathbb{p}(r)setminus {(0)}$, where   $mathbb{p}(r)$ is...

Let G be a group acting via ring automorphisms on an integral domain R. A ring-theoretic property of R is said to G-invariant, if $$R^G$$ also has the property, where $$R^G=\{r\in \ | \sigma (r)=r \text {for all} \in G\},$$ fixed action. In this paper we prove following classes rings are invariant under operation $$R\rightarrow R^G:$$ locally pqr domains, Strong G-domains, Hilbert rings, S-stro...