IJPAM: Volume 25, No. 2 (2005)

REPRESENTATIONS OF FUZZY GROUPS AND ALGEBRAS

Chuang Peng
Department of Mathematics
Morehouse College
830 Westview Drive, S.-W., Atlanta, GA 30314, USA
e-mail: cpeng@morehouse.edu


Abstract.This paper contains some preliminary work on representations of fuzzy groups and algebras. The work is based on the notion of $L$-subset (or $L$-subgroup, $L$-submodule, etc.), where $L$ is a lattice. It proves homological properties of $L$-modules. It defines fuzzy projective and injective submodules of a module, and shows some of the important properties of fuzzy (sub)modules. The paper also studies the Hom functor of fuzzy modules and defines short and long exact sequences of fuzzy modules and the cohomology from the derived chain complexes.

Received: September 11, 2005

AMS Subject Classification: 20N25, 08A72

Key Words and Phrases: $L$-set, fuzzy, representation, homology, cohomology

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 2