In this paper we shall apply modules of generalized fractions to extend the notion of the grade of an ideal, and to obtain characterizations of Gorenstein rings.

‎‎Let $R$ be a non-commutative ring with unity‎. ‎The commuting graph‎ of $R$ denoted by $Gamma(R)$‎, ‎is a graph with a vertex set‎ ‎$Rsetminus Z(R)$ and two vertices $a$ and $b$ are adjacent if and only if‎ $ab=ba$‎. ‎In this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. It is shown that‎, ‎$Gamma(R)$ is the disjoint ...

tetrazole-containing compounds have been the subject of much recent research because of theirpotential as high energy density materials (hedms). in this work, theoretical studies on the 1htetrazolylderivatives of tetrahedrane were done at the density functional theory (dft) method withthe 6-31g(d) basis set without any symmetrical restrictions in order to find the structural andenergetically pr...

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.

the freiheitssatz of magnus for one-relator groups is one of the cornerstones of combinatorial group theory. in this short note which is mostly expository we discuss the relationship between the freiheitssatz and corre-sponding results in free power series rings over fields. these are related to results of schneerson not readily available in english. this relationship uses a faithful representa...

Using a t-norm T , the notion of T -fuzzy subhypernear-rings (for short TFSrings) of hypernear-rings is introduced and some of their properties are investigated. Also we study the structure of TFS-rings under direct product.

Introduction: Many previous studies have proved that the anatomical features of cervix can affect the success of artificial insemination. These characteristics differ in sheep breeds. This study aimed to describe the anatomical features of cervix in Zell ewes; the only tailed sheep in Iran. Methods: Eighty nonpregnant and clinically healthy reproductive tracts of adult Zel sheep were collected...

Objective: In a previous work, we showed that asafoetida essential oil (AEO), from oleo-gum resin of Ferula asafoetida L. from the Apiaceae family, has a vasodilatory effect. This effect was both endothelium-dependent and endothelium-independent. The present study was designed to determine whether potassium channels and intracellular calcium release contribute to AEO-i...