Abstract
In this paper, we present a new notion of fuzzy ideals : called weakly prime fuzzy ideal. Let R be a commutative ring with non-zero identity. A nonconstant fuzzy ideal µ of R is called weakly prime fuzzy ideal if 0_t != x_r y_s ∈ µ implies x_r ∈ µ or y_s ∈ µ for all t ∈ (0, µ(0)]. We investigate some properties of this notion. Morever, it is established relations between weakly prime ideals and weakly prime fuzzy ideals of commutative rings.
Keywords
Prime (order theory)
Mathematics
Commutative ring
Associated prime
Ideal (ethics)
Prime ideal
Fuzzy logic
Commutative property
Pure mathematics
Boolean prime ideal theorem
Minimal ideal
Radical of an ideal
Discrete mathematics
Primary ideal
Identity (music)
Maximal ideal
Combinatorics
Principal ideal ring
Computer science
Physics
Law
Artificial intelligence
Subject Areas
Fuzzy and Soft Set Theory
·Management Science and Operations Research ·Social Sciences
Fuzzy Logic and Control Systems
·Artificial Intelligence ·Physical Sciences
Advanced Algebra and Logic
·Computational Theory and Mathematics ·Physical Sciences
Citations by Year
2023: 1
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