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...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

in this paper, we introduce the notion of ($epsilon $, $epsilon $ $vee$ q_{k})− fuzzy subnear-ring which is a generalization of ($epsilon $, $epsilon $ $vee$ q)−fuzzy subnear-ring. we have given examples which are ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy ideals but they are not ($epsilon $, $epsilon $ $vee$ q)−fuzzy ideals. we have also introduced the notions of ($epsilon $, $epsilon $ $vee$ ...

In this paper, we determine completely the initial Fitting ideal of the minus part of the ideal class group of an abelian number field over Q up to the 2-component. This answers an open question of Mazur and Wiles [11] up to the 2-component, and proves Conjecture 0.1 in [8]. We also study Brumer’s conjecture and prove a stronger version for a CM-field, assuming certain conditions, in particular...

in this paper, by introducing two virtual decision-making units (dmus) called ideal dmu (idmu) and anti-ideal dmu (admu) with fuzzy inputs-outputs, the efficiency evaluation of dmus are done by fuzzy data envelopment analysis (fdea). therefore, we evaluate dmus from the perspective of the best and worst possible relative efficiency. for each dmu two efficiencies are calculated while inputs and ...

Detection of intensity flashes in the blowfly photoreceptor is limited by photon noise in the input signal as well as noise contributed by transduction components within the photoreceptor. Our analysis uses an ideal observer and a model of blowfly phototransduction to compute the threshold for optimal detection of intensity flashes as background intensity varies. We find that detection threshol...

Multilinear maps have become popular tools for designing cryptographic schemes since a first approximate realisation candidate was proposed by Garg, Gentry and Halevi (GGH). This construction was later improved by Langlois, Stehlé and Steinfeld who proposed GGHLite which offers smaller parameter sizes. In this work, we provide the first implementation of such approximate multilinear maps based ...