Some categorical aspects of BCH-algebras

Categorical equivalence of some algebras

We show that two lattices are categorically equivalent if and only if they are isomorphic or dually isomorphic. Two normal bands are categorically equivalent if and only if they are isomorphic or antiisomorphic. The same result holds for finite bands as well. We also obtain corollaries for rectangular bands and semilattices.

Categorical Aspects of von Neumann Algebras and AW ∗ - algebras Sander

We take a look at categorical aspects of von Neumann algebras, constructing products, coproducts, and more general limits, and colimits. We shall see that exponentials and coexponentials do not exist, but there is an adjoint to the spatial tensor product, which takes the role of coexponent. We then introduce the class of AW*-algebras and try to see to what extend these categorical constructions...

On Pseudo BCH-algebras

As a generalization of BCH-algebras, the notion of pseudo BHalgebra is introduced, and some of their properties are investigated. The notions of pseudo subalgebra, pseudo ideals, and pseudo atoms in pseudo BCH-algebras are introduced. Characterizations of their properties are provided. Mathematics Subject Classification: 06F35, 03G25

Smarandache BCH - Algebras

We introduce the notion of Smarandache BCH-algebra and Smarandache (fresh, clean and fantastic) ideals, some example are given and related properties are investigated. Relationship between Q-Smarandache (fresh, clean and fantastic) ideals and other types of ideals are given. Extension properties for Q-Smarandache (fresh, clean and fantastic) ideals are established.

Partial Inner Product Spaces: Some Categorical Aspects