Abstract
The goal of this paper is to give a definition of a generalization of fuzzy prime $\Gamma $-ideals in $\Gamma $-rings by introducing fuzzy 2-absorbing $\Gamma $-ideals and fuzzy weakly completely 2-absorbing $\Gamma $-ideals of commutative $\Gamma $-rings and to give their properties. Furthermore, we give a diagram which transition between definitions of fuzzy 2-absorbing $\Gamma $-ideals of a $\Gamma $-ring. Finally, we introduce fuzzy quotient $\Gamma $-ring of $R$ induced by the fuzzy weakly completely 2-absorbing $\Gamma $-ideal is a $2$-absorbing $\Gamma $-ring.
Keywords
Mathematics
Fuzzy logic
Prime (order theory)
Pure mathematics
Quotient
Ring (chemistry)
Commutative ring
Generalization
Ideal (ethics)
Discrete mathematics
Algebra over a field
Commutative property
Combinatorics
Mathematical analysis
Computer science
Artificial intelligence
Chemistry
Subject Areas
Fuzzy and Soft Set Theory
·Management Science and Operations Research ·Social Sciences
Advanced Algebra and Logic
·Computational Theory and Mathematics ·Physical Sciences
Fuzzy Logic and Control Systems
·Artificial Intelligence ·Physical Sciences
Loading…