Extended Ideals in MV-Algebras

F. Forouzesh ()
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F. Forouzesh: Faculty of Mathematics and Computing, Higher Education Complex of Bam, Kerman, Iran

New Mathematics and Natural Computation (NMNC), 2022, vol. 18, issue 03, 559-571

Abstract: In this paper, we introduce the notion of extended of an ideal associated to a subset of an MV-algebra A and investigate the related properties. A characterization of this extended ideal is given. We show that I is stable ideal relative to B ⊆ A such that B ∩ I = ∅ if and only if A/I is chain MV-algebra. Finally, the class S(B) of all stable ideals relative to B ⊆ A is also a complete Heyting algebra, for an MV-algebra A.

Keywords: Stable ideal; extended ideal; Boolean ideal; Heyting algebra (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S1793005722500284

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