A generalization of UP-algebras: Weak UP-algebras

Abstract

Many logical algebras such as BE-, KU- and BCC-algebras have their weak version as generalization. It is known that a CI-algebra is a weak version of a BE-algebra, a JU-algebra is a weak version of a KU-algebra, and a BZ-algebra is a weak version of a BCC-algebra. In this paper, we introduce the concept of weak UP-algebras as a generalization of UP-algebras, and investigate its basic properties. Additionally, some types of ideals in this type of algebras are introduced and analyzed.

Keywords

• up-algebra
• weak up-algebra
• closed wup-ideal
• (★)-ideal
• ag-ideal
• strong ideal
• regular ideal
• associative ideal
• t-ideal