Foruzesh, F., Bedrood, M. (2016). On some classes of expansions of ideals in $MV$-algebras. Algebraic Structures and Their Applications, 3(2), 31-47.

Fereshteh Foruzesh; Mahta Bedrood. "On some classes of expansions of ideals in $MV$-algebras". Algebraic Structures and Their Applications, 3, 2, 2016, 31-47.

Foruzesh, F., Bedrood, M. (2016). 'On some classes of expansions of ideals in $MV$-algebras', Algebraic Structures and Their Applications, 3(2), pp. 31-47.

Foruzesh, F., Bedrood, M. On some classes of expansions of ideals in $MV$-algebras. Algebraic Structures and Their Applications, 2016; 3(2): 31-47.

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

^{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.

[1] A. Filipoiu, G. Georgescu, A. Lettieri, Maximal MV -algebras, Mathware, soft comput., 4 (1997), pp. 53–62. [2] C. C. Chang, Algebraic analysis of many valued logic, Trans. Amer. Math. Soc., 88 (1958), pp. 467–490. [3] C. C. Chang, A new proof of the completeness of the Lukasiewicz axioms,Trans. Amer. Math. Soc., 93 (1959), pp. 74–80. [4] R. Cignoli, I. M. L. D’Ottaviano, D. Mundici, Algebraic foundations of many valued reasoning, Kluwer Academic, Dordrecht, (2000). [5] F. Forouzesh, E. Eslami, A. Borumand saeid, On obstinate ideals in MV −algebras, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. Vol. 76, (2014), pp. 53–62. [6] C. S. Hoo, S. Sessa, Implicative and Boolean ideals of MV-algebras, Math. Japon. 39 (1994), pp. 215-219. [7] S. Motamed, J. Moghaderi, Expansions of filters in Residuated lattices, International Journal of Contem- porary Mathematical siences, Vol. 11 (2016), pp. 9-15. [8] D. Piciu, Algebras of fuzzy logic, Ed. Universitaria Craiova (2007).