Suppose that is an innnite set and k is a natural number. Let ] k denote the set of all k-subsets of and let F be a eld. In this paper we study the FSym(()-submodule structure of the permutation module F] k. Using the representation theory of nite symmetric groups, we show that every submodule of F] k can be written as an intersection of kernels of certain FSym(()-homomorphisms F] k ?! F] l for...

Submodule construction is the problem of finding a new submodule which, together with a given submodule, provides a behavior that conforms to a given desired global behavior. A new formulation of this problem and its solution in first-order logic is presented, and it is shown how the known solutions to this problem in the context of various communication paradigms and specification formalisms c...

An R-module A is called GF-regular if, for each a ∈ A and r ∈ R, there exist t ∈ R and a positive integer n such that r(n)tr(n)a = r(n)a. We proved that each unitary R-module A contains a unique maximal GF-regular submodule, which we denoted by M GF(A). Furthermore, the radical properties of A are investigated; we proved that if A is an R-module and K is a submodule of A, then MGF(K) = K∩M GF(A...

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 $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semi...