july 2023 $Z^{\circ}$-ideals and $Z$-ideals in $MV$-algebras
Mahta Bedrood, Farhad Sajadian, Giacomo Lenzi, Arsham Borumand Saeid
Bull. Belg. Math. Soc. Simon Stevin 30(1): 51-65 (july 2023). DOI: 10.36045/j.bbms.211109

Abstract

The set of zero divisors of an $MV$-algebra is investigated. It is proved that the set of all zero divisors of an $MV$-algebra $A$ is the union of all prime ideals of $A$. Next, $Z^{\circ}$-ideals and $Z$-ideals are introduced and their properties are studied. We examine the relationship between them and their relationship with the minimal prime ideals. We study their behavior under homomorphism of $ MV$-algebras. Also, we investigate in what conditions the annihilator of an ideal is a $Z^{\circ}$-ideal and $Z$-ideal.

Citation

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Mahta Bedrood. Farhad Sajadian. Giacomo Lenzi. Arsham Borumand Saeid. "$Z^{\circ}$-ideals and $Z$-ideals in $MV$-algebras." Bull. Belg. Math. Soc. Simon Stevin 30 (1) 51 - 65, july 2023. https://doi.org/10.36045/j.bbms.211109

Information

Published: july 2023
First available in Project Euclid: 6 August 2023

Digital Object Identifier: 10.36045/j.bbms.211109

Subjects:
Primary: 06B10 , 06D35

Keywords: $MV$-algebra , ($Z^{\circ}$, $Z$, prime) ideal , hyperarchimedean , zero divisor

Rights: Copyright © 2023 The Belgian Mathematical Society

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Vol.30 • No. 1 • july 2023
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