This paper addresses the problem of designing a submodule of a given system ofcommunicating I/O automata. The problem may be formulated mathematically by theequation (C||X)rA under the constraint IX=In, where C represents the specification of theknown part of the system, called the context, A represents the specification of the whole system,X represents the specification of the ...

Quasi-polycyclic (QP for short) codes over a finite chain ring R are generalization of quasi-cyclic codes, and these can be viewed as an R[x]-submodule $${\mathcal {R}}_m^{\ell }$$ , where {R}}_m:= R[x]/\langle f\rangle $$ f is monic polynomial degree m R. If factors uniquely into coprime basic irreducibles, then their algebraic structure allow us to characterize the generator polynomials minim...

We present an algorithm to compute the primary decomposition of a submodule N of the free module Z[x1, . . . , xn]. For this purpose we use algorithms for primary decomposition of ideals in the polynomial ring over the integers. The idea is to compute first the minimal associated primes of N , i.e. the minimal associated primes of the ideal Ann(Z[x1, . . . , xn]/N ) in Z[x1, . . . , xn] and the...

A right Johns ring is a Noetherian in which every ideal annihilator. It known that RR the Jacobson radical J(R)J(R) of nilpotent and Soc(R)(R) an essential RR. Moreover, Kasch, is, simple RR-module can be embedded For M∈RM∈R-Mod we use concept MM-annihilator define module (resp. quasi-Johns) as MM such submodule MM-annihilator. called quasi-Johns if any set submodules satisfies ascending chain ...

The notion of the square submodule of a module M over an arbitrary commutative ring R, which is denoted by RM, was introduced by Aghdam and Najafizadeh in [3]. In fact, RM is the R−submodule of M generated by the images of all bilinear maps on M. Furthermore, given a submodule N of an R−module M, we say that M is nil modulo N if μ(M×M) ≤ N for all bilinear maps μ on M. The main question about t...

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...

We study the H n ( 0 ) -module S ? ? due to Tewari and van Willigenburg, which was constructed using new combinatorial objects called standard permuted composition tableaux decomposed into cyclic submodules. First, we show that every direct summand appearing in their decomposition is indecomposable characterize when indecomposable. Second, find characteristic relations among 's expand image of ...

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...