We study the notions of nuclearity and exactness for module maps on C∗-algebras which are C∗-module over another C∗-algebra with compatible actions examine finite approximation properties such C∗-modules. prove versions results Kirchberg Choi–Effros. As a concrete example, we extend dimensional reduced von Neumann algebras countable discrete groups to these operator inverse semigroups structure...

During growth on crystalline cellulose, the thermophilic bacterium Caldicellulosiruptor bescii secretes several cellulose-degrading enzymes. Among these enzymes is CelA (CbCel9A/Cel48A), which is reported as the most highly secreted cellulolytic enzyme in this bacterium. CbCel9A/Cel48A is a large multi-modular polypeptide, composed of an N-terminal catalytic glycoside hydrolase family 9 (GH9) m...

let $r$ be a commutative ring. in this paper we assert some properties of finitely generated comultiplication modules and fitting ideals of them.

we show that every semi-artinian module which is contained in a direct sum of finitely presented modules in $si[m]$, is weakly co-semisimple if and only if it is regular in $si[m]$. as a consequence, we observe that every semi-artinian ring is regular in the sense of von neumann if and only if its simple modules are $fp$-injective.

let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

‎A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$‎. ‎It is not known whether a direct summand of an FI-extending module is also FI-extending‎. ‎In this study‎, ‎it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?

we call a module  essentially retractable if homr for all essential submodules n of m. for a right fbn ring r, it is shown that: (i)  a non-zero module  is retractable (in the sense that homr for all non-zero ) if and only if certain factor modules of m are essentially retractable nonsingular modules over r modulo their annihilators. (ii)  a non-zero module  is essentially retractable if and on...

‎we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel‎, ‎that is‎, ‎every simple right $r$-module has a flat $b$-cover‎. ‎we give some properties of such rings along with examples‎. ‎we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...

Over the past decade, great progress has been made in the static modular verification of C code by means of separation logic-based program logics. However, the runtime guarantees offered by such verification are relatively limited when the verified modules are part of a whole program that also contains unverified modules. In particular, a memory safety error in an unverified module can corrupt ...

We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...