@misc{10481/108940,
year = {2025},
month = {12},
url = {https://hdl.handle.net/10481/108940},
abstract = {There is a correspondence between equivalence classes of fuzzy ideals, on a commutative
ring, and decreasing gradual ideals. In this paper, we explore how to construct a fuzzy
ideal starting from any decreasing gradual ideal σ. To achieve this, we consider an interior
operator, σ
d
, and a closure operator, σ
e
, and show that the pair (σ
d
, σ
e
) is always an F-pair,
which defines a fuzzy ideal. Furthermore, this correspondence, and its inverse, preserves
sums, intersections and products. This therefore provides an algebraic framework for
studying fuzzy ideals. In particular, prime fuzzy ideals and weakly prime fuzzy ideals
have their counterparts in the theory of decreasing gradual ideals, offering us a new
perspective on these particular objects. One of the main objectives is to characterize fuzzy
prime ideals using single fuzzy elements and gradual ideals.},
organization = {MCIN/AEI/10.13039/50110001103 (IMAG-María de Maeztu, grant CEX2020-001105-M)},
publisher = {MDPI},
keywords = {Gradual commutative ring},
keywords = {Fuzzy commutative ring},
keywords = {Prime ideal},
title = {Fuzzy and Gradual Prime Ideals},
doi = {10.3390/math13243998},
author = {Jara Martínez, Pascual and Giar Mohamed, Salwa},
}