Abstract
In this paper, we introduce the notion of quasi-pseudo-BL algebras as the generalization of pseudo-BL algebras and quasi-pseudo-MV algebras. First, we investigate the properties of quasi-pseudo-BL algebras and show the subdirect product composition of any quasi-pseudo-BL algebra. Especially, some properties of good quasi-pseudo-BL algebras are presented. Second, we discuss the filters of quasi-pseudo-BL algebras and prove that there exists a bijective correspondence between normal filters and filter congruences on a quasi-pseudo-BL algebra. The properties of some special filters are also discussed. Finally, we study the ideals of quasi-pseudo-BL algebras and investigate some connections between ideals and filters of a quasi-pseudo-BL algebra.
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Funding
This study was funded by the National Natural Science Foundation of China (Grant No. 11501245), China Postdoctoral Science Foundation (No. 2017M622177) and Shandong Province Postdoctoral Innovation Projects of Special Funds (No. 201702005).
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Communicated by A. Di Nola.
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Chen, W., Wang, H. Filters and ideals in the generalization of pseudo-BL algebras. Soft Comput 24, 795–812 (2020). https://doi.org/10.1007/s00500-019-04528-9
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DOI: https://doi.org/10.1007/s00500-019-04528-9