Let $R\ $be a commutative ring with $1\neq0$ and $M$ be an $R$-module. Suppose that $S\subseteq R\ $is multiplicatively closed set of $R.\ $Recently Sevim et al. in \cite{SenArTeKo} introduced the notion $S$-prime submodule which is generalization prime used them to characterize certain classes rings/modules such as submodules, simple modules, torsion free modules,\ $S$-Noetherian modules etc. ...

The full-bridge submodules (FB-SMs) in hybrid modular multilevel converters need to absorb the enormous energy stored dc side and arm inductors during fault blocking, which may lead severe overvoltage. An energy-absorbing branch (EAB) composed of metal oxide varistor (MOV) thyristors is proposed this letter. No extra power loss produced by EAB normal operation. can a part reduce absorbed FB-SMs...

In the above article [1] , there is an inconsistency in defining equation $HV$ login phase and mutual authentication as shown Figs. 3 5, respectively. Cloud Server $CS$ of Fig. 3, equal to $h\left(RV_{i} \oplus CID_{i} \| HS\right)$ which $RV_{i} CID_{i}$ $h\left(VID_{i}\right)$ described 2 $HS=h\left(S_{i, t}^{\prime}\right)$ previous line $HV=h\left(RV_{i} . Then, User $U_{i}$ $V K_{x}=h\left...

In [4] B. M. Schein considered systems of the form ( ; o; n),where is a set of functions closed under the composition "o" of functions (and hence ( ; o) is a function semigroup) and the set theoretic subtraction "n" (and hence is a subtraction algebra in the sense of [1]). He proved that every subtraction semigroup is isomorphic to a di erence semigroup of invertible functions. B. Zelinka [5] d...

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...

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 ...