Let $R$ be a commutative ring and $M$ an $R$-module. A submodule $N$ of is called d-submodule $($resp., fd-submodule$)$ if $\ann_R(m)\subseteq \ann_R(m')$ $\ann_R(F)\subseteq \ann_R(m'))$ for some $m\in N$ finite subset $F\subseteq N)$ $m'\in M$ implies that N.$ Many examples, characterizations, properties these submodules are given. Moreover, we use them to characterize modules satisfying Prop...

It is proven that each indecomposable injective module over a valuation domain R is polyserial if and only if each maximal immediate extension R̂ of R is of finite rank over the completion R̃ of R in the R-topology. In this case, for each indecomposable injective module E, the following invariants are finite and equal: its Malcev rank, its Fleischer rank and its dual Goldie dimension. Similar res...

In this article we introduce μ-filtered fuzzy module with a family of fuzzy submodules. It shows the relation between μ-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the μ-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull’s intersection theorem of fuzzy ideals by using concept μ-adic completion.

Subsingular vectors of the N=2 superconformal algebras were discovered, and examples given, in 1996. Shortly afterwards Semikhatov and Tipunin claimed to have obtained a complete classification of the N=2 subsingular vectors in the paper ‘The Structure of Verma Modules over the N=2 Superconformal algebra’, hep-th/9704111, published in CMP 195 (1998) 129. Surprisingly, the only explicit examples...

Let R be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented R-modules that are closed under extensions. We also classify abelian subcategories of arbitrary R-modules that are closed under extensions and coproducts, when R is commutative and Noetherian. The method relies on comparison with ...

As it can be noticed, haptic interfacing, among other rendering capabilities, takes an important place. This particular focus meets the Touch-HapSys objectives in better understand haptics and its relation with the other modalities. From a pure technical point-of-view, the framework is divided in three main modules; each of them is further subdivided in as many submodules as needed. The I-Touch...