Abstract
In this paper, we mainly consider three classes of quantum B-algebras such as locally unital quantum B-algebras, two-sided quantum B-algebras and implication-commutative quantum B-algebras. We first prove that a quantum B-algebra can be embedded into a unital quantum B-algebra if and only if it is a locally unital quantum B-algebra. Next, we introduce two-sided (implication-commutative) quantum B-algebras and give their characterization. Based on which we finally investigate the filters of quantum B-algebras.
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