A Structured Document Algebra (SDA) defines modules with variation points and how such modules compose. The basic operations are module addition and replacement. Repeated addition can create nested module structures. SDA also allows the decomposition of modules into smaller parts. In this paper we show how SDA modules can be used to deal algebraically with Software Product Lines (SPLs). In part...

This paper outlines the research conducted to develop and evaluate a Visual Art Education tool (APH-Pensil), based on the fundamental design theory. This tool consists of six modules. The Art element module help students acquire skills in creating lines, space and colour; the Design module, help students acquire skills to identify harmony, balance, emphasis, contrast, rhythm, variations and int...

The ground field k is algebraically closed and of characteristic zero. Let G be a semisimple simply-connected algebraic group over k and U a maximal unipotent subgroup of G. One of the fundamental invariant-theoretic facts, which goes back to Hadžiev [9], is that k[G/U ] is a finitely generated k-algebra and regarded as G-module it contains every finite-dimensional simple G-module exactly once....

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...

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 $emph{h}$...

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...

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In the past three decades, the ML module system has been the focal point of tremendous interest in the research community. The combination of parameterized modules and fine-grain data abstraction control have proven to be quite powerful in practice. Mainstream languages have slowly adopted features inspired by the ML module system. However, programmers have run into various limitations and comp...

Let g be a finite-dimensional simple Lie algebra over C of type An, and let U be the q-analogue of its universal enveloping algebra defined by Drinfel’d [4] and Jimbo [6]. According to [9, 3.5.6, 6.2.3 & 6.3.4], for each dominant weight λ in the weight lattice of g there is an irreducible, finite-dimensional highest weight U -module V (λ) with highest weight λ. Kashiwara [7] and Lusztig [8] hav...