量子B-代数的可逆元

On the Invertible Elements of Quantum B-Algebras

量子B-代数是一种非可换的逻辑代数,它可以看作是Quantale的一种推广.量子B-代数包含了多种蕴含代数,其中偏序群就是一种特殊的量子B-代数.主要研究了量子B-代数的可逆元,证明了所有可逆元构成一个偏序群.

Quantum B-algebras are a class of non-commutative logical algebras, which can be seen as a generalization of quantales. Quantum B-algebras cover a majority of implication algebras such as partially ordered groups which are a special class of quantum B-algebras. In this paper, the invertible elements of quantum B-algebras are investigated, and it is shown that the set of all invertible elements of quantum B-algebras is a partially ordered group.