几类量子B-代数上的滤子
Filters on some classes of quantum B-algebras
摘要：
本文继续研究量子B-代数，重点研究积分量子B-代数上的滤子。然后，我们研究过滤器设置的伪箍。首先，我们建立了一个嵌入的cartesion积的极的伪箍本身。其次，给出了伪环亚直约的充分条件。我们还将Kondo和Turunen的结果推广到非交换剩余$\vee$ -半格的情形，即如果剩余$\vee$ -半格$A$的素滤子与$\vee$ -素滤子重合，则$A$必是伪MTL-代数.
英文摘要：
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 $\vee$-semilattices that, if prime filters and $\vee$-prime filters of a residuated $\vee$-semilattice $A$ coincide, then $A$ must be a pseudo MTL-algebra.
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