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@article{1320845, author = {Botur, Michal and Paseka, Jan}, article_location = {NEW YORK}, article_number = {12}, doi = {http://dx.doi.org/10.1007/s10773-015-2608-0}, keywords = {Quantale; Quantum B-algebra; Filter; Prime filter; Pseudo-hoop; Pseudo MTL-algebra}, language = {eng}, issn = {0020-7748}, journal = {International Journal of Theoretical Physics}, title = {Filters on Some Classes of Quantum B-Algebras}, volume = {54}, year = {2015} }
TY - JOUR ID - 1320845 AU - Botur, Michal - Paseka, Jan PY - 2015 TI - Filters on Some Classes of Quantum B-Algebras JF - International Journal of Theoretical Physics VL - 54 IS - 12 SP - 4397-4409 EP - 4397-4409 PB - Springer SN - 00207748 KW - Quantale KW - Quantum B-algebra KW - Filter KW - Prime filter KW - Pseudo-hoop KW - Pseudo MTL-algebra N2 - 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. ER -
BOTUR, Michal a Jan PASEKA. Filters on Some Classes of Quantum B-Algebras. \textit{International Journal of Theoretical Physics}. NEW YORK: Springer, 2015, roč.~54, č.~12, s.~4397-4409. ISSN~0020-7748. Dostupné z: https://dx.doi.org/10.1007/s10773-015-2608-0.
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