The Koszul dual of a Sklyanin algebra A is a nite dimensional graded algebra depending on an elliptic curve, a translation automorphism, and an integer n 3; it may be deened as Ext A (k;k). The representation theory and structure of these algebras is studied by using the functor Ext A (?; k) to transfer results from the Sklyanin algebras to the nite dimensional algebras. We show that their repr...

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...

The Auslander-Reiten conjecture is a notorious open problem about the vanishing of Ext modules. In Cohen-Macaulay complete local ring R with parameter ideal Q, holds for if and only it residue R/Q. former part this paper, we study R/Qℓ in connection that R, prove equivalence them case where Gorenstein ℓ≤dim⁡R. latter part, generalize result minimal multiplicity by J. Sally. Due to these two our...

In this note, we provide several characterizations of regular local rings in positive characteristics, in terms of the Hilbert-Kunz multiplicity and its higher Tor counterparts ti = lim n→∞ l(Tori(k, f n R))/p . We also apply the characterizations to improve a recent result by Bridgeland and Iyengar in the characteristic p case. Our proof avoids using the existence of big CohenMacaulay modules,...

Self-reconngurable robots consist of a set of one or more identical autonomous modules that can adapt their shape and function to tasks. We describe a module that can function as a climbing robot, a manipula-tor, or a leg in a multi-legged walker. This module can make autonomous transitions between these states. We present the control algorithms that enable our robot to be a versatile navigator...

(1) Utilizing a Braid group action on a completion of Uq(ŝln+1), an algebra homomorphism from the toroidal algebra Uq(sln+1,tor) (n ≥ 2) with fixed parameter to a completion of Uq(ĝln+1) is obtained. (2) The toroidal actions by Saito induces a level 0 U ′ q(ŝln+1) action on level 1 integrable highest weight modules of Uq(ŝln+1). Another level 0 U ′ q(ŝln+1) action is defined by Jimbo, et al., i...

Let $R$ be a ring and $M$ be a right $R$-module. In this paper, we give some properties of self-cogeneratormodules. If $M$ is self-cogenerator and $S = End_{R}(M)$ is a cononsingular ring, then $M$ is a$mathcal{K}$-module. It is shown that every self-cogenerator Baer is dual Baer.

The homology of Lie algebras is closely related to the cyclic homology of associative algebras [LQ]. In [L] the first author constructed a "noncommutative" analog of Lie algebra homology which is, similarly, related to Hochschild homology [C, L]. For a Lie algebra g this new theory is the homology of the complex C,(g) ... ~ ~| g|-+ ... ~1 ~ k, whose boundary map d is given by the formula d(gl|1...

Introduction: Liver plays a pivotal role in glucose and lipid homeostasis. This study was undertaken to evaluate the effects of L. acanthodes hydro-alcoholic extract administration on the liver functional and histological parameters in hyperglycemic rats. Methods: Twenty-four male Wistar rats were randomly allocated into four groups control, hyperglycemic (STZ), hyperglycemic + insulin (STZ...