A General Approach To Chain Condition in $BL$-Algebras

Jamal Kazemiasl, Farhad Khaksar Haghani, Shahram Heidarian

In this paper, we present a general definition of the notion of Noetherian and Artinian $BL$-algebra and present a more comprehensive insight at the chain conditions in $BL$-algebras. We derive some theorems which generalize the existence results. We give an axiomatic approach to the notion of being Noetherian and Artinian, which is also applicable to other algebraic structures. We use a theoretical approach to define arithmetic notion that is also possible for other algebraic devices. In this study, we only focus to $BL$-algebras.