Top-down design methodology is one of the widely used approaches to the design of complex concurrent systems. In this approach, the speciication of a system is decomposed into a set of submodules whose concurrent behavior is equivalent to that of the system speciication. The following problem is of particular importance when using this methodology: given the speciication of a system and some of...

In a finite-dimensional vector space, every subspace is finite-dimensional and the dimension of a subspace is at most the dimension of the whole space. Unfortunately, the naive analogue of this for modules and submodules is wrong: (1) A submodule of a finitely generated module need not be finitely generated. (2) Even if a submodule of a finitely generated module is finitely generated, the minim...

Let be a distance-regular graph of diameter D. Let X denote the vertex set of and let Y be a nonempty subset of X . We define an algebra T = T (Y ). This algebra is finite dimensional and semisimple. If Y consists of a single vertex then T is the corresponding subconstituent algebra defined by P. Terwilliger. We investigate the irreducible T -modules. We define endpoints and thin condition on i...

let $r$ be a commutative ring. the purpose of this article is to introduce a new class of ideals of r called weakly irreducible ideals. this class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. the relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

in this paper we introduce the notions of g∗l-module and g∗l-module whichare two proper generalizations of δ-lifting modules. we give some characteriza tions and properties of these modules. we show that a g∗l-module decomposesinto a semisimple submodule m1 and a submodule m2 of m such that every non-zero submodule of m2 contains a non-zero δ-cosingular submodule.

The notion of final theory results from a contrasting understanding of physical reality. Currently, different approaches aim to unify the four forces of nature and discuss whether a final theory may be possible. A key feature of a final theory is irreducibility, however this property has not been seriously exploited. In the paper we present an irreducible mathematical theory that describes phys...

We construct families of irreducible representations for a class of quantum groups Uq(fm(K,H). First, we realize these quantum groups as Hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for Uq(fm(K,H)). Second, we study the relationship between Uq(fm(K,H)) and Uq(fm(K)). As a result, any finite dimensional weight representation of Uq(fm(K,H))...

In this paper we introduce the notion of join irreducibility in the context of bilattices and present a procedural semantics for bilattice based logic programs which uses as its basis the join irreducible elements of the knowledge part of the bilattice The join irreducible elements in a bilattice represent the primitive bits of information present within the system In bilattices which have the ...

‎let $r$ be a domain with quotiont field $k$‎, ‎and‎ ‎let $n$ be a submodule of an $r$-module $m$‎. ‎we say that $n$ is‎ ‎powerful (strongly primary) if $x,yin k$ and‎ ‎$xymsubseteq n$‎, ‎then $xin r$ or $yin r$ ($xmsubseteq n$‎ ‎or $y^nmsubseteq n$ for some $ngeq1$)‎. ‎we show that a submodule‎ ‎with either of these properties is comparable to every prime‎ ‎submodule of $m$‎, ‎also we show tha...