$L$-fuzzy prime ideals and maximal $L$-fuzzy ideals of a poset

The Fuzzy Prime Spectrum of Partially Ordered Sets

“…Te present paper is the continuation of Assaye Alaba et al's work [11][12][13], and so we will follow the same notations, defnitions, and results on fuzzy ideals, u-fuzzy ideals, fuzzy flters, l-fuzzy flters, prime fuzzy ideals, prime fuzzy flters, maximal fuzzy ideals, and maximal fuzzy flters in a poset.…”

“…Conversely, assume that μ c ∈ FF l (Z). Ten, by Teorem 3.3 of [13], it is enough to check that the set…”

“…Tey ofer a more comprehensive understanding of the structure and relationships between elements, allowing for a deeper exploration of the underlying order relations. Tey further investigate the primness and maximality conditions in the class of fuzzy ideals in a general poset in [13]. In addition, they obtained sufcient conditions for the existence of fuzzy prime ideals in a poset as in the lattice of its fuzzy ideals.…”

The Commutator of Fuzzy Congruences in Universal Algebras

“…In 1971, A.Rosenfeld [3] applied this theory and has formulated the concept of a fuzzy subgroup of a group. Since then, many researchers have been studying fuzzy subalgebras of several algebraic structures such as rings (see [4][5][6]), modules (see [7][8][9]), vector spaces (see [10,11]), lattices (see [12][13][14][15][16][17]), pseudo-complemented semi-lattice (see [18]), posets (see [19,20]), MS-algebras (see [21][22][23][24]), universal algebras (see [25][26][27][28]), etc.…”