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- W4312965728 abstract "In this paper, bounded commutative residuated quasi-ordered quasi-monoids (bounded commutative Rq $$ell $$ -monoids, for short) as a generalization of bounded commutative residuated lattice ordered monoids (bounded commutative R $$ell $$ -monoids, for short) are introduced. First, the properties of bounded commutative Rq $$ell $$ -monoids are investigated and the relations among quasi-MV algebras, quasi-BL algebras and bounded commutative Rq $$ell $$ -monoids are discussed. Second, the filters and weak filters of bounded commutative Rq $$ell $$ -monoids are defined. The one-to-one correspondence between the set of filters and the set of filter congruences on a bounded commutative Rq $$ell $$ -monoid is given. Moreover, the relation between the set of weak filters and the set of congruences on a bounded commutative Rq $$ell $$ -monoid is showed. As an application of the study, the properties of the quotient algebra with respect to a weak filter are investigated. Finally, the properties of some special sets in a bounded commutative Rq $$ell $$ -monoid are showed." @default.
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- W4312965728 date "2022-01-01" @default.
- W4312965728 modified "2023-09-26" @default.
- W4312965728 title "A Generalization of Bounded Commutative R$$ell $$-Monoids" @default.
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- W4312965728 doi "https://doi.org/10.1007/978-981-19-7510-3_14" @default.
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