the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

we define and studyco-noetherian dimension of rings for which the injective envelopeof simple modules have finite krull-dimension. this  is a moritainvariant dimension that measures how far the ring is from beingco-noetherian. the co-noetherian dimension of certain rings,including commutative rings, are determined. it is shown that the class ${mathcal w}_n$ of rings with co-noetherian dimension...

Crocus sativus L. (saffron) is a widely used food additive for its color and taste. The hypotensive effects of saffron have been shown in previous studies. The aim of this study was to evaluate the mechanism of vasodilatory effects induced by saffron on isolated rat aorta.To study the vasodilatory effects of saffron aqueous extract (0.5, 1 and 2 mg/mL), isolated rat thoracic aorta rings were co...

statement of the problem: implant-retained overdenture can improve the stability of dentures and prevent bone loss. overdenture-wearing patients need special hygiene care. purpose: the aim of this study was to evaluate the effects of various denture cleansers on the retention of dio orange o-rings. method and materials : in this experimental study, 40 dio orange o-rings were divided into 4 grou...

The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...

BACKGROUND A "saddle-shaped" mitral annulus with an optimal ratio between annular height and commissural diameter may reduce leaflet and chordal stress and is purported to be conserved across mammalian species. Whether annuloplasty rings maintain this relationship is unknown. METHODS AND RESULTS Twenty-three adult sheep underwent implantation of radiopaque markers on the left ventricle and mi...

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.

We define and studyco-Noetherian dimension of rings for which the injective envelopeof simple modules have finite Krull-dimension. This  is a Moritainvariant dimension that measures how far the ring is from beingco-Noetherian. The co-Noetherian dimension of certain rings,including commutative rings, are determined. It is shown that the class ${mathcal W}_n$ of rings with co-Noetherian dimension...

In this paper, we introduce the new notion of strongly J-clean rings associated with polynomial identity g(x) = 0, as a generalization of strongly J-clean rings. We denote strongly J-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-J-clean rings. Next, we investigate some properties of strongly g(x)-J-clean.