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EBL-algebras

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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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Acknowledgements

The author is grateful to the referees for their careful reading and suggestions which improve the paper highly. This study was partly funded by National Natural Science Foundation of China [No. 11701339] and Natural Science Foundation of Shandong Province [ZR2018BA003, ZR2018MA003].

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Correspondence to Hongxing Liu.

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Communicated by A. Di Nola.

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Liu, H. EBL-algebras. Soft Comput 24, 14333–14343 (2020). https://doi.org/10.1007/s00500-020-05235-6

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  • DOI: https://doi.org/10.1007/s00500-020-05235-6

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