alzheimer’s disease (ad) is a uniquely human disorder. although the pathogenesis of ad is not fully understood, growing evidence indicates that the deposition of beta-amyloid (aβ) and the local reactions of various cell types to this protein play major roles in the development of the disease. in the present study transgenic mice expressing mutant amyloid precursor protein (app) has been used. t...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

In this paper, we show how to conjointly use module theory and constructive homological algebra to obtain general conditions for a matrix R of functional operators (e.g., differential/shift/time-delay operators) to be equivalent to a block-triangular or block-diagonal matrix R (i.e., conditions for the existence of unimodular matrices V and W satisfying that R = V R W ). These results allow us ...

By an F -semi-linear G-representation we mean an F -space V with a (k-linear) G-action such that (a v) = a v for any 2 G, v 2 V and a 2 F . This is the same as a module over the algebra F hGi := F ZZ[G] with evident action of F and the diagonal action of G. If G acts on F faithfully, then F hGi is a central k-algebra. Semi-linear G-representations nite-dimensional over F form an abelian tensor ...

We characterize the initial terms under a diagonal term order of the supersymmetric Schur/Weyl module S(V V ) associated to a row-convex shape D. We show the biwords corresponding to the initial terms of S are closed under dual-Knuth equivalence and that the recording tableaux for these words are decomposable in the sense of [10]. We consider the natural action of bases of S in which the elemen...

By a coalgebra over the commutative ring K or a K-coalgebra, we understand a cocommutative, coassociative K-coalgebra with counit. More explicitly we mean a K-module C equipped with maps &C+C&C, subject to the requirement (where we write @ for OK) that the following diagrams commute: CLC@C where the vertical arrow is the one which switches the factors; CAC@C 1 CC38 C@C e@'CtC@C@C, where we have...

a module $m$ is called $emph{h}$-cofinitely supplemented if for every cofinite submodule $e$ (i.e. $m/e$ is finitely generated) of $m$ there exists a direct summand $d$ of $m$ such that $m = e + x$ holds if and only if $m = d + x$, for every submodule $x$ of $m$. in this paper we study factors, direct summands and direct sums of $emph{h}$-cofinitely supplemented modules. let $m$ be an $emph{h}$...

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...