Filters on Some Classes of Quantum B-Algebras
| Autoři | |
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| Rok publikování | 2015 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | International Journal of Theoretical Physics |
| Fakulta / Pracoviště MU | |
| Citace | |
| Doi | http://dx.doi.org/10.1007/s10773-015-2608-0 |
| Obor | Obecná matematika |
| Klíčová slova | Quantale; Quantum B-algebra; Filter; Prime filter; Pseudo-hoop; Pseudo MTL-algebra |
| Popis | In this paper, we continue the study of quantum B-algebras with emphasis on filters on integral quantum B-algebras. We then study filters in the setting of pseudo-hoops. First, we establish an embedding of a cartesion product of polars of a pseudo-hoop into itself. Second, we give sufficient conditions for a pseudohoop to be subdirectly reducible. We also extend the result of Kondo and Turunen to the setting of noncommutative residuated a-semilattices that, if prime filters and a-prime filters of a residuated a-semilattice A coincide, then A must be a pseudo MTL-algebra. |
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