On Liu algebras: a new composite structure of the BCL⁺ algebras and the semigroups

Yonghong Liu


This paper offers a new algebra, which is called the Liu algebra (which is named after author), because of its origin in BCL⁺ algebras, and connections between BCL⁺ algebras and semigroups, have more complex structures, or, saying a composite structure. While Liu algebras are dividing into two distinct parts that are structurally independent, we think there are good reasons to mash them up, can be enforced by algebraic operations on distributive laws. Here we introduce several new notions (i.e., ideal, funnel and deductive systems in Liu algebras). We show that if G and H be two algebras, if G ≅ H, then (L; *, •, 1) is an order isomorphism, and discuss some properties for Liu algebras.

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Published: 2017-02-27

How to Cite this Article:

Yonghong Liu, On Liu algebras: a new composite structure of the BCL⁺ algebras and the semigroups, Journal of Semigroup Theory and Applications, Vol 2017 (2017), Article ID 2

Copyright © 2017 Yonghong Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Journal of Semigroup Theory and Applications

ISSN 2051-2937

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