Abstract

Cubic set is a structure with two components which has been applied in the conditions of $\beta-$ideals. This paper presents the notion of cubic fuzzy $\beta-$ideal of a $\beta-$algebra. In addition that, the notion of cubic $(\overline{a},b)$-translation, cubic $\mu $-multiplication were presented. Further, some engrossing results of cubic $\beta-$ideals with the combination of multiplication and translation were investigated.

Keywords and Phrases

$\beta-$algebra, $\beta-$ideals, Cubic $\beta-$ideal, cubic ideals, Cubic translation, Cubic multiplication.

A.M.S. subject classification

06F35, 03G25, 08A72, 03E72.

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