On pseudo-\(e\)BE-algebras. (English) Zbl 1490.06013
Summary: In this paper, we define the notion of a pseudo-eBE-algebra as an extension of a pseudo-BE-algebra, and it is studied in detail. The construction of an eBE-algebra from a pseudo-eBE-algebra is given. Further, the notions of filters and ideals are considered. The classes of distributive and commutative pseudo-eBE-algebras are introduced and investigated. We prove that for a distributive pseudo-eBE-algebra filters coincide with ideals. Also, some types of filters are defined and the relationship between these is investigated.
MSC:
| 06F35 | BCK-algebras, BCI-algebras |
| 03G25 | Other algebras related to logic |
| 06B10 | Lattice ideals, congruence relations |
Keywords:
(pseudo) BE-algebra; (distributive, commutative) pseudo-eBE-algebra; ideal; (quasi, simple, pseudo) filterReferences:
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