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10-08-2020 | Foundations

EBL-algebras

Author: Hongxing Liu

Published in: Soft Computing | Issue 19/2020

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Abstract

In this paper, we define the notion of EBL-algebras, which are generalizations of BL-algebras and EMV-algebras. The notions of ideals, congruences and filters in EBL-algebras are introduced, and their mutual relationships are investigated. There is a one-to-one correspondence between the set of all ideals in an EBL-algebra and the set of all congruences on an EBL-algebra. Moreover, we give a representation theorem on EBL-algebras. Every proper EBL-algebras under some condition can be embedded into an EBL-algebras with a top element as an ideal.

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Title: EBL-algebras
Author: Hongxing Liu
Publication date: 10-08-2020
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 19/2020
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-020-05235-6

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