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; ]].

Sensory stimuli entering the nervous system follow particular paths of processing, typically separated (segregated) from the paths of other modal information. However, sensory perception, awareness and cognition emerge from the combination of information (integration). The corticocortical networks of cats and macaque monkeys display three prominent characteristics: (i) modular organisation (fac...

We prove a new structural result for the spherical Tits building attached to GLnK for many number fields K, and more generally for the fraction fields of many Dedekind domains O: the Steinberg module Stn(K) is generated by integral apartments if and only if the ideal class group cl(O) is trivial. We deduce this integrality by proving that the complex of partial bases of O is Cohen–Macaulay. We ...

‎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...

The main aim of this paper is to provide a description of parameter test ideals of local Cohen-Macaulay rings of prime characteristic p. The nature of this description will be such that it will allow us to give an algorithm for producing these ideals. The results in this paper will follow from an analysis of Frobenous maps on injective hulls of the residue fields of the rings under consideratio...

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...

let $r$ be a commutative ring. we write $mbox{hom}(mu_a, nu_b)$ for the set of all fuzzy $r$-morphisms from $mu_a$ to $nu_b$, where $mu_a$ and $nu_b$ are two fuzzy $r$-modules. we make$mbox{hom}(mu_a, nu_b)$ into fuzzy $r$-module by redefining a function $alpha:mbox{hom}(mu_a, nu_b)longrightarrow [0,1]$. we study the properties of the functor $mbox{hom}(mu_a,-):frmbox{-mod}rightarrow frmbox{-mo...