‎We say that a module $M$ is a emph{cms-module} if‎, ‎for every cofinite submodule $N$ of $M$‎, ‎there exist submodules $K$ and $K^{'}$ of $M$ such that $K$ is a supplement of $N$‎, ‎and $K$‎, ‎$K^{'}$ are mutual supplements in $M$‎. ‎In this article‎, ‎the various properties of cms-modules are given as a generalization of $oplus$-cofinitely supplemented modules‎. ‎In particular‎, ‎we prove tha...

In this paper, we nd the relationships between module contractibility of aBanach algebra and its ideals. We also prove that module contractibility ofa Banach algebra is equivalent to module contractibility of its module uniti-zation. Finally, we show that when a maximal group homomorphic image ofan inverse semigroup S with the set of idempotents E is nite, the moduleprojective tensor product l1...

 The class of ads modules with the SIP (briefly‎, ‎$SA$-modules) is studied‎. ‎Various conditions for a module to be $SA$-module are given‎. ‎It is proved that for a quasi-continuous module $M$‎, ‎$M$ is a UC-module if and only if $M$ is an $SA$-module‎. ‎Also‎, ‎it is proved that the direct sum of two $SA$-modules as $R$-modules is an $SA$-module when $R$ is the sum of the annihilators of thes...

a module $m$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $m$ into $m$. we prove that all right (left) modules over a ring are coretractable if and only if the ring is morita equivalent to a finite product of local right and left perfect rings.

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

Mitochondrial F1Fo-ATP synthase generates the bulk of cellular ATP. This molecular machine assembles from nuclear- and mitochondria-encoded subunits. Whereas chaperones for formation of the matrix-exposed hexameric F1-ATPase core domain have been identified, insight into how the nuclear-encoded F1-domain assembles with the membrane-embedded Fo-region is lacking. Here we identified the INA compl...

Two important trends of modern modular robotics research are module size reduction and the increase of the total number of modules in a robotic system. Smaller and simpler modules are expected to be cheaper if fabricated in bulk and easier to selectively replace in a modular system in case of failures. Stochastic methods of modular robots assembly and reconfiguration enable individual module si...

A laboratory continuous feed biofilm reactor, comprising a bulk fluid reactor, a biofilm plastic module, a feed tank, and pneumatic devices and controls, was operated for a total period of 257 days, including seeding time, to treat domestic-strength synthetic wastewater under increasing ammonium nitrogen (NH(4)(+)--N) loading rates, ranging from 0.17+/-0.01 (0.71+/-0.06 gm(-2)d(-1)) to 0.70+/-0...

In this paper we study the module contractibility ofBanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. Also weinvestigate module contractibility of Banach algebras with theconcept of the module diagonal.