m-Polar cubic p(q and a)-ideals of BCI-algebras

Abstract

In this paper, we apply the [Formula: see text]-polar cubic structures on BCI-algebras. We first present the ideas of [Formula: see text]-polar cubic [Formula: see text]-ideals, [Formula: see text]-polar cubic [Formula: see text]-ideals and [Formula: see text]-polar cubic [Formula: see text]-ideals in BCI-algebras. Then we prove that [Formula: see text]-polar cubic [Formula: see text]([Formula: see text] and [Formula: see text])-ideals are [Formula: see text]-polar cubic ideals, but the converse assertion is not true, and an example is provided in this support. We define the conditions under which [Formula: see text]-polar cubic ideals coincide with [Formula: see text]-polar cubic [Formula: see text]([Formula: see text] and [Formula: see text])-ideals. The associated properties of [Formula: see text]-polar cubic [Formula: see text]-ideals, [Formula: see text]-polar cubic [Formula: see text]-ideals, and [Formula: see text]-polar cubic [Formula: see text]-ideals are also examined. Furthermore, we consider [Formula: see text]-polar cubic [Formula: see text]([Formula: see text] and [Formula: see text])-ideals in terms of [Formula: see text]([Formula: see text] and [Formula: see text])-ideals of BCI-algebras.