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 ...

Herbivores can alter plant physiology through the induction of abnormal wood formation. Feeding by some insects induces the formation of false rings, a band of thick-walled latewood cells within the earlywood portion of the tree ring that reduces water transport. Hemlock woolly adelgid (Adelges tsugae Annand) and elongate hemlock scale (Fiorinia externa Ferris) are invasive insects that both f...

Our previous linear analysis presents a new instability driven by dust coagulation in protoplanetary disks. The has the potential to concentrate grains into rings and assist planetesimal formation. In this series of papers, we perform numerical simulations investigate nonlinear outcome instability. paper (Paper I), first conduct local demonstrate existence Linear growth observed is good agreeme...

we give a survey of recent applications of group rings to combinatorics and tocryptography, including their use in the di erential cryptanalysis of block ciphers.

The abundance and composition of glycerol dibiphytanyl glycerol tetraether (GDGT) and glycerol tribiphytanyl glycerol tetraether (GTGT) lipids were determined as a function of growth phase as a proxy for nutrient availability, the pH of growth medium, and incubation temperature in cultures of the thermoacidophile Picrophilus torridus. Regardless of the cultivation condition, the abundance of GD...

The transport of Balbiani ring (BR) premessenger RNP particles in the larval salivary gland cells of the dipteran Chironomus tentans can be followed using electron microscopy. A BR RNP particle consists of an RNP ribbon bent into a ringlike structure. Upon translocation through the nuclear pore complex (NPC), the ribbon is straightened and enters the central channel of the NPC with the 5' end o...

An efficient N-heterocyclic carbene (NHC) catalyzed sulfenylation reaction of α,β-unsaturated aldehydes with N-(arylthio)phthalimide has been developed. A wide variety of α-thioenals can be obtained with good to excellent yields and excellent Z-configuration.