Open AccessTense Operators on BL-algebras and its Applications
Author(s) -
Akbar Paad
Publication year - 2021
Publication title -
bulletin of the section of logic
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.225
H-Index - 13
eISSN - 2449-836X
pISSN - 0138-0680
DOI - 10.18778/0138-0680.2021.11
Subject(s) - congruence relation , mathematics , future tense , present tense , pure mathematics , algebra over a field , linguistics , philosophy , verb
In this paper, the notions of tense operators and tense filters in \(BL\)-algebras are introduced and several characterizations of them are obtained. Also, the relation among tense \(BL\)-algebras, tense \(MV\)-algebras and tense Boolean algebras are investigated. Moreover, it is shown that the set of all tense filters of a \(BL\)-algebra is complete sublattice of \(F(L)\) of all filters of \(BL\)-algebra \(L\). Also, maximal tense filters and simple tense \(BL\)-algebras and the relation between them are studied. Finally, the notions of tense congruence relations in tense \(BL\)-algebras and strict tense \(BL\)-algebras are introduced and an one-to-one correspondence between tense filters and tense congruences relations induced by tense filters are provided.