A General Approach To Chain Condition in BL-Algebras

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.