The use of homological and homotopical devices, such as Tor and AndréQuillen homology, have found substantial use in characterizing commutative algebras. The primary category setting has been differentially graded algebras and modules, but recently simplicial categories have also proved to be useful settings. In this paper, we take this point of view up a notch by extending some recent uses of ...

For ontology reuse and integration, a number of approaches have been devised that aim at identifying modules, i.e., suitably small sets of “relevant” axioms from ontologies. Here we consider three logically sound notions of modules: MEX modules, only applicable to inexpressive ontologies; modules based on semantic locality, a sound approximation of the first; and modules based on syntactic loca...

In this paper, we establish automorphic properties and asymptotic behaviors of characters due to Kac–Wakimoto pertaining to s (m|n)∧ highest weight modules in the case m = n, extending work of Bringmann and Ono (Math Ann 345:547–558, 2009) and Bringmann and Folsom (submitted) which pertains to the case m > n.

Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz’ approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum homogeneous vector bundles are classified and explicitly constructed by using the theory of projective modules.

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...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

The ML module system enables flexible development of large software systems by its support of nested structures, functors and signatures. In spite of this flexibility, however, recursion between modules is prohibited, since dependencies between modules must accord with the order of definitions. As a result of this constraint, programmers may have to consolidate conceptually separate components ...

In a trace-based world, the modular specification, verification, and control of live systems require each module to be receptive; that is, each module must be able to meet its liveness assumptions no matter how the other modules behave. In a real-time world, liveness is automatically present in the form of diverging time. The receptiveness condition, then, translates to the requirement that a m...

Extending work of Puninski, Puninskaya and Toffalori in [PPT07], we show that if V is an effectively given valuation domain then the theory of all V -modules is decidable if and only if there exists an algorithm which, given a, b ∈ V , answers whether a ∈ rad(bV ). This was conjectured in [PPT07] for valuation domains with dense value group where it was proved for valuation domains with dense a...

We provide several crucial technical extensions of the theory stable independence notions in accessible categories. In particular, we describe circumstances under which a notion can be transferred from subcategory to category as whole, and examine number applications categories groups modules, extending results [16]. prove, too, that hypotheses [11], immediately yields higher-dimensional [26].