Filters on Some Classes of Quantum B-Algebras
| Authors | |
|---|---|
| Year of publication | 2015 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Theoretical Physics |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1007/s10773-015-2608-0 |
| Field | General mathematics |
| Keywords | Quantale; Quantum B-algebra; Filter; Prime filter; Pseudo-hoop; Pseudo MTL-algebra |
| Description | 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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