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.

We describe a natural structure of an abelian intertwining algebra (in the sense of Dong and Lepowsky) on the direct sum of the untwisted vertex operator algebra constructed from the Leech lattice and its (unique) irreducible twisted module. When restricting ourselves to the moonshine module, we obtain a new and conceptual proof that the moonshine module has a natural structure of a vertex oper...

To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projec...

Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum....

This paper deals with the localization module extension for various platform to support locating in the interior. Any mobile devices (vehicles) can be equipped with a GPS module for location, but in areas with high density in the building interior or city centers a location using GPS is not suitable due to insufficient signal. The solution for these sites can be seen in use of existing WiFi inf...

Several proof-assistants rely on the very formal basis of Pure Type Systems. However, some practical issues raised by the development of large proofs lead to add other features to actual implementations for handling namespace management, for developing reusable proof libraries and for separate veriication of distincts parts of large proofs. Unfortunately, few theoretical basis are given for the...