On some classes of expansions of ideals in $MV$-algebras

Foruzesh, Fereshteh; Bedrood, Mahta

On some classes of expansions of ideals in $MV$-algebras

Document Type : Research Paper

Authors

Fereshteh Foruzesh ¹
Mahta Bedrood ²

¹ Faculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran.

² Department of Mathematics , Shahid Bahonar University Kerman, Iran.

Abstract

In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (\tau,\sigma)- $primary, $ (\tau,\sigma)$-obstinate and $ (\tau,\sigma)$-Boolean in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (\tau,\sigma)$-obstinate ideal of an $ MV-$ algebra is $ (\tau,\sigma)$-primary and $ (\tau,\sigma)$-Boolean. In particular, we define an expansion $ \sigma_{y} $ of ideals in an $ MV-$algebra. A characterization of expansion ideal with respect to $ \sigma_{y} $ is given. Finally, we show that the class $ C(\sigma_{y}) $ of all constant ideals relative to $ \sigma_{y} $ is a Heyting algebra.

Keywords

References

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