we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

Let (W, S) be a finite Coxeter system and A := Z[0] be the group algebra of a finitely generated free abelian group 0. Let H be an Iwahori-Hecke algebra of (W, S) over A with parameters vs . Further let K be an extension field of the field of fractions of A and KH be the extension of scalars. In this situation Kazhdan and Lusztig have defined their famous basis and the so called left cell modul...

An aspect-oriented programming (AOP) is for modularising a crosscutting concern so that it can be easily attached and detached to/from software. Because of this functionality, AOP is one of key technologies for enabling evolvable software. However, critics have been mentioning that AOP makes modular reasoning difficult since join points where an aspect and an object are connected to each other ...

A characterization of module alphabets with the Hamming weight EP (abbreviation for Extension Property) had been settled. A thoughtfully constructed piece-of-art example by J.A.Wood ([7]) finished the tour. In 2009, in [8], Frobenius bimodules were proved to satisfy the EP with respect to symmetrized weight compositions. In [4], the embeddability in the character group of the ambient ring R was...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...

Let  be a commutative ring and  be a unitary  module. We define a semi prime sub module of a module and consider various properties of it. Also we define semi-radical of a sub module of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.

Latency-insensitive systems were recently proposed by Carloni et al. for the design of single-clock systems-on-a-chip (SoC’s) using predesigned IP blocks. The goal of this paper is to extend and generalize latency-insensitive systems in such a way that they can be applied to GALS architectures with multiple clocks. In particular, we propose two extensions. The first extension allows each synchr...

The Distributed Virtual Communication Machine (DVCM) is an extensible communication architecture for tightly-coupled clusters of workstations (COWs) connected by high-speed networks. The DVCM is designed for off-theshelf network interface cards equipped with communication coprocessors. Its main component is an “active backplane” implemented in firmware running on the coprocessors. This “backpla...

We study certain filtrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warfield. To indicate the consequences of our analysis, suppose that g is a complex classical simple Lie superalgebra and that E is an indecomposable injective g-module with nonzero (and so necessarily s...