In [1, 2], we initiated the BCL-algebras and BCL⁺ -algebras. Later on, we
introduced the partial orders of a BCL⁺ -algebra [4] and topological BCL⁺
-algebras [6]. In 2013, Deena and Rodyna [3] extended the study of the
deformation to characterize BCL-algebras. Deena [8] recently introduced the notion of soft BCL-algebras. This paper is a study on algebraic structure of BCL⁺
-algebra, which is used for the extended distributive law, that is left (resp. right)
distribution rule, left (resp. right) weakly distribution rule, left (resp. right)
strongly distribution rule, left (resp. right) quasi-distribution rules. We give some
characterizations of distributive BCL⁺ -algebras. Here, the remainder of the paper
is organized as follows:
In [1, 2], we initiated the BCL-algebras and BCL⁺ -algebras. Later on, weintroduced the partial orders of a BCL⁺ -algebra [4] and topological BCL⁺-algebras [6]. In 2013, Deena and Rodyna [3] extended the study of thedeformation to characterize BCL-algebras. Deena [8] recently introduced the notion of soft BCL-algebras. This paper is a study on algebraic structure of BCL⁺-algebra, which is used for the extended distributive law, that is left (resp. right)distribution rule, left (resp. right) weakly distribution rule, left (resp. right)strongly distribution rule, left (resp. right) quasi-distribution rules. We give somecharacterizations of distributive BCL⁺ -algebras. Here, the remainder of the paperis organized as follows:
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