A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules.Over the past several years QTAG-modules have been the subject of intense investigation yet there is much to explore.The impetus for these efforts stems from the fact that the rings considered here are almost restriction free....

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)ysubseteq P$ for $x, yin M$, implies that $xin P$ or $yin P$. In this paper, we study more properties of strongly prime submodules. It is shown that a finitely generated $R$-module $M$ is Artinian if and only if $M$ is Noetherian and every st...

In this paper branching rules for the fundamental representations of the symplectic groups in positive characteristic are found. The submodule structure of the restrictions of the fundamental modules for the group Sp2n(K) to the naturally embedded subgroup Sp2n−2(K) is determined. As a corollary, inductive systems of fundamental representations for Sp∞(K) are classified. The submodule structure...

In previous research we extended the submodule construction techniques to cover a more expressive and compact behavioral model that handles data through parameterized interactions, state variables, and simple transition guards. The model was based on extended Input/Output Automata, and the algorithm on the Chaos concept. In this paper we generalize these extensions and improve the submodule con...

The submodule construction problem (SCP) as stated and formulated by Merlin and Bochmann [P. Merlin, G.V. Bochmann, On the construction of submodule specification and communication protocols, ACM Trans. Prog. Lang. Sys., 5(1) (1983) 1–25] is considered: given the specification of a system (module) and that of its n 2 1 submodules, determine the specification of the nth submodule that together w...

Let be a module over commutative ring with identity. Before studying the concept of Strongly Pseudo Nearly Semi-2-Absorbing submodule, we need to mention ideal and basics that you study submodule. Also, introduce several characteristics submodule in classes multiplication modules other types modules. We also had no luck because is not ideal. it noted under conditions, which this faithful module...

Let $N$ be a submodule of a module $M$ and a minimal primary decomposition of $N$ is known‎. ‎A formula to compute Baer's lower nilradical of $N$ is given‎. ‎The relations between classical prime submodules and their nilradicals are investigated‎. ‎Some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.