In this paper, we are mainly concerned with the Cartan determinant conjecture and the no loop conjecture. If A is an artin algebra of finite global dimension, the first conjecture claims that the Cartan determinant of A is equal to 1, while the second one states that every simple A-module admits only the trivial self-extension. Among numerous partial solutions to these conjectures such as those...

The Hilbert function of a module over a positively graded algebra is of quasi-polynomial type (Hilbert–Serre). We derive an upper bound for its grade, i. e. the index from which on its coefficients are constant. As an application, we give a purely algebraic proof of an old combinatorial result (due to Ehrhart, McMullen and Stanley). 1. HILBERT QUASIPOLYNOMIALS Let K be a field, and R a positive...

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...

Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I ⊆ S let gI be the corresponding semi-simple subalgebra of g. Denote by WI the Weyl group of gI and let w◦ and w I ◦ be the longest elements of W and WI , respectively. In this paper we show that the answer to Kostant’s problem, i.e. whether the universal enveloping algebra surjects on...

Modern space modules are susceptible to EM radiation from both external and internal sources within the space module. Since the EM waves for various operations are frequently in the high-frequency domain, asymptotic raytheoretic methods are often the most optimal choice for deterministic EM field analysis. In this work, surface modeling of a typical manned space module is done by hybridizing a ...

This paper concerns curves on non-commutative schemes, hereafter called quasi-schemes. A quasi-scheme X is identiied with the category ModX of quasi-coherent sheaves on it. Let X be a quasi-scheme having a regularly embedded hypersurface Y. Let C be a curve on X which is in \good posi-tion" with respect to Y (see Deenition 5.1)|this deenition includes a requirement that X be far from commutativ...

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 $emph{h}$...

The main goal of this paper is to introduce a new class in the category modules. It called quasi-invertibility monoform (briefly QI-monoform) This modules generalization Various properties and another characterization QI-monoform are investigated. So, we prove that an R-module M if only for each non-zero homomorphism f:M E(M), kernel not quasi-invertible submodule M. Moreover, cases under which...

We make a new multivariate generalization of the type A monomial space of a single variable. It is different from the previously introduced type A space of several variables which is an sl(M + 1) module, and we thus call it type A′. We construct the most general quasi-solvable operator of (at most) second-order which preserves the type A′ space. Investigating directly the condition under which ...