BCI/BCK- quantum algebra
Abstract
The paper contains an investigation of the notion of BCI-algebras and BCK-algebras. The concept of quantale was created in 1984 to develop a framework for non-commutative spaces and quantum mechanics with a view toward non-commutative logic. Implicational algebras like pseudo-BCK algebras are quantum B-algebras, and every quantum B-algebra can be recovered from its spectrum which is a quantale. [25].
A brief introduction to quantum mechanics is given. A new generalization of BCI/BCK-algebra and some there properties have been given. The BCI- quantum algebra and BCk- quantum algebra have been studied. The BCI- Lie algebra and BCK- Lie algebra are introduced. Various examples have been given.
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References
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