In this paper we characterize the radical of an arbitrary‎ ‎submodule $N$ of a finitely generated free module $F$ over a‎ ‎commutatitve ring $R$ with identity‎. ‎Also we study submodules of‎ ‎$F$ which satisfy the radical formula‎. ‎Finally we derive‎ ‎necessary and sufficient conditions for $R$ to be a‎ ‎Pr$ddot{mbox{u}}$fer domain‎, ‎in terms of the radical of a‎ ‎cyclic submodule in $Rbigopl...

In this paper, we consider the problem of extending existing submodule construction techniques that have been developed for finite state models into more expressive and compact behavioral models that handle data through parameterized interactions, state variables and simple guards. We provide a behavioral model based on extended Input-Output Automata and describe an algorithm that provides the ...

Let R be a commutative ring with identity and let M be an infinite unitary R-module. (Unless indicated otherwise, all rings are commutative with identity 1 ̸ = 0 and all modules are unitary.)ThenM is called a Jónsson module provided every proper submodule of M has smaller cardinality than M. Dually, M is said to be homomorphically smaller (HS for short) if |M/N| < |M| for every nonzero submodule...

Abstract: Let be a commutative ring and be a unitary module. We define a semiprime submodule of a module and consider various properties of it. Also we define semi-radical of a submodule 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.  

Let $R$ be a commutative ring with identity. A proper submodule $N$ of an $R$-module $M$ is an n-submodule if $rmin N~(rin R, min M)$ with $rnotinsqrt{Ann_R(M)}$, then $min N$. A number of results concerning n-submodules are given. For example, we give other characterizations of n-submodules. Also various properties of n-submodules are considered.

A module MR is called right principally quasi-Baer (or simply right p.q.-Baer) if the right annihilator of a principal submodule of R is generated by an idempotent. Let R be a ring. Let α be an endomorphism of R and MR be a α-compatible module and T = R[[x;α]]. It is shown that M [[x]]T is right p.q.-Baer if and only if MR is right p.q.-Baer and the right annihilator of any countably-generated ...

A new bidirectional isolated Zero-VoltageSwitching (ZVS) DC-DC converter with nonpulsating input and output current is proposed. This converter is ideally suited for battery charging application and is applied as a submodule in a battery storage system based on a modular multilevel converter (MC). The current output of the proposed DC-DC converter enables small current ripple for directly inter...

Each symplectic group over the field of two elements has two exceptional doubly transitive actions on sets of quadratic forms on the defining symplectic vector space. This paper studies the associated 2-modular permutation modules. Filtrations of these modules are constructed which have subquotients which are modules for the symplectic group over an algebraically closed field of characteristic ...