On the free S^{ω}_{1} -algebras

In this paper, we introduce the notion of states and state operators on residuated skew lattices and investigate some related properties of them. The relationships between state operators and states on residuated skew lattices are discussed. We prove that every Bosbach state on a residuated skew lattice is a Riecan state and with an example we show that there is a Riecan state on a residuated skew lattice which is not a Bosbach state. Also, some conditions are given for a Riecan state on residuated skew lattice to be a Bosbach state. We present different types of state residuated skew lattices, like weak, strong, simple, local and state-morphism residuated skew lattices. Any weak state-morphism residuated skew lattice is a strong state residuated skew lattice and converse is true under an extra condition.

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States on Residuated Skew Lattices

Koohnavard

Saeid

2021

New Math. and Nat. Computation

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New definition of MV-semimodules

Goraghani

Borzooei

Ahn

2021

IFS

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In recent years, A. Di Nola et al. studied the notions of MV-semiring and semimodules and investigated related results [9, 10, 12, 26]. Now in this paper, by using an MV-semiring and an MV-algebra, we introduce the new definition of MV-semimodule, study basic properties and find some examples. Then we study A-ideals on MV-semimodules and Q-ideals on MV-semirings, and by using them, we study the quotient structures of MV-semimodule. Finally, we present the notions of prime A-ideal, torsion free MV-semimodule and annihilator on MV-semimodule and we study the relations among them.

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Construction of some algebras of logic by using fuzzy ideals in mv-modules

Bakhshi

Ahn

Jun

et al. 2023

IFS

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We study the lattice structure of fuzzy A-ideals in an mv-module M (fai (M), symbolically) and show that it is a complete Heyting lattice and so the set of its pseudocomplements forms a Boolean algebra. In the sequel, the properties of fuzzy congruences in an mv-module are investigated and using them some structural theorems are stated and proved. Finally, it is proved that fai (M) can be embedded into the lattice of fuzzy congruences.

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On the free S^{ω}_{1} -algebras

Abstract: One and two-generated free M V -algebras are algebraically described in the variety generated by perfect M V -algebras.

Cited by 3 publications

References 15 publications

States on Residuated Skew Lattices

States on Residuated Skew Lattices

New definition of MV-semimodules

Construction of some algebras of logic by using fuzzy ideals in mv-modules

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