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Commutative pseudo BE-algebras | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 10، دوره 13، شماره 1، اردیبهشت 2016، صفحه 131-144 اصل مقاله (340.42 K) | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2016.2293 | ||
| نویسنده | ||
L. C. Ciungu 
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| Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242-1419, Usa | ||
| چکیده | ||
| The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties. We generalize some results proved by A. Walendziak for the case of commutative BE-algebras. We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-algebras also hold for commutative pseudo BE-algebras. For example, any finite commutative pseudo BE-algebra is a BE-algebra, and any commutative pseudo BE-algebra is a join-semilattice. Moreover, if a commutative pseudo BE-algebra is a meet-semilattice, then it is a distributive lattice. We define the pointed pseudo-BE algebras, and introduce and study the relative negations on pointed pseudo BE-algebras. Based on the relative negations we construct two closure operators on a pseudo BE-algebra. We also define relative involutive pseudo BE-algebras, we investigate their properties and prove equivalent conditions for a relative involutive pseudo BE-algebra. We define the relative Glivenko property for a relative good pseudo BE-algebra and show that any relative involutive pseudo BE-algebra has the relative Glivenko property. | ||
| کلیدواژه‌ها | ||
| Pseudo BE-algebra؛ Pseudo BCK-algebra؛ Commutative pseudo BCK-algebra؛ Commutative pseudo BE-algebra؛ Pointed pseudo BE-algebra؛ Relative involutive pseudo BE-algebra؛ Relative Glivenko property | ||
| مراجع | ||
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