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...

a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...

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...

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.

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 ...

It is shown numerically that strange matter rings permit a continuous transition to the extreme Kerr black hole. The multipoles as defined by Geroch and Hansen are studied and suggest a universal behaviour for bodies approaching the extreme Kerr solution parametrically. The appearance of a ‘throat region’, a distinctive feature of the extreme Kerr spacetime, is observed. With regard to stabilit...

The global minimum structure of borospherene (B40) is a cage, comprising two hexagonal and four heptagonal rings. Born-Oppenheimer Molecular Dynamics simulations show that continuous conversions in between six and seven membered rings take place. The activation energy barrier for such a transformation is found to be 14.3 kcal · mol(-1). The completely delocalized σ- and π-frameworks, as well as...

6 Introduction to Affine Schemes 2 6.1 Rings and Modules of Fractions . . . . . . . . . . . . . . . . . 2 6.2 The Spectrum of a Unital Commutative Ring . . . . . . . . . 5 6.3 The Spectrum of a Quotient Ring . . . . . . . . . . . . . . . . 7 6.4 The Spectrum of a Ring of Fractions . . . . . . . . . . . . . . 9 6.5 Intersections of Prime Ideals . . . . . . . . . . . . . . . . . . . 11 6.6 Topolo...