Abstract
We study the class of pseudo-BL-algebras whose every maximal filter is normal. We present an equational base for this class and we extend these results for the class of basic pseudo hoops with fixed strong unit. This is a continuation of the research from Botur et al. (Soft Comput 16:635–644, doi:10.1007/s00500-011-0763-7, 2012).
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Notes
We note that an \(\ell \)-group is a group \(\mathbf G=(G;+,-,0,\le )\) with a neutral element 0 and endowed with a partial order \(\le \) such that (1) \(a\le b\) implies \(c+a+d\le c+b+d\) for all \(c,d\in G\), (2) G under \(\le \) is a lattice. For more info about \(\ell \)-groups, see e.g., Darnel (1995) and Glass (1999).
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Acknowledgments
The authors are very indebted to an anonymous referee for his/her careful reading and suggestions which helped to improve the readability of the paper.
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Communicated by A. Di Nola.
Both authors gratefully acknowledge the support by GAČR 15-15286S. AD thanks also Slovak Research and Development Agency under contract APVV-0178-11, Grant VEGA No. 2/0059/12 SAV.
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Botur, M., Dvurečenskij, A. On pseudo-BL-algebras and pseudo-hoops with normal maximal filters. Soft Comput 20, 439–448 (2016). https://doi.org/10.1007/s00500-015-1793-3
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DOI: https://doi.org/10.1007/s00500-015-1793-3
Keywords
- Pseudo-BL-algebra
- Pseudo-MV-algebra
- Maximal filter
- Pseudo-hoop
- Unital basic pseudo-hoop
- Normal-valued pseudo-BL-algebra