let $r$ be a commutative noetherian ring with non-zero identity, $fa$ an ideal of $r$, and $x$ an $r$--module. here, for fixed integers $s, t$ and a finite $fa$--torsion $r$--module $n$, we first study the membership of $ext^{s+t}_{r}(n, x)$ and $ext^{s}_{r}(n, h^{t}_{fa}(x))$ in the serre subcategories of the category of $r$--modules. then, we present some conditions which ensure the exi...

we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...

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; ]].

BioC is a recently created XML format to share text data and annotations, and an accompanying input/output library to promote interoperability of data and tools for natural language processing of biomedical text. This article reports the use of BioC to address a common challenge in processing biomedical text information-that of frequent entity name abbreviation. We selected three different abbr...

A smart transducer network hosts various nodes with different functionality. Our approach offers the possibility to design different smart transducer nodes as a system-on-a-chip within the same platform. Key elements are a set of code compatible processor cores which can be equipped with several extension modules. Due to the fact that all processor cores are code compatible, programs developed ...

the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...

an r-module m is called strongly noncosingular if it has no nonzero rad-small (cosingular) homomorphic image in the sense of harada. it is proven that (1) an r-module m is strongly noncosingular if and only if m is coatomic and noncosingular; (2) a right perfect ring r is artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

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We describe a modular modelling approach permitting curation, updating, and distributed development of modules through joined community effort overcoming the problem of keeping a combinatorially exploding number of monolithic models up to date. For this purpose, the effects of genes and their mutated alleles on downstream components are modeled by composable, metadata-containing Petri net model...