Type 2 of internal direct products of UP (BCC)-algebras

This article delves into the innovative application of the internal direct product (IDP) in the framework of UP (BCC)-algebras, introducing two novel types: the standard IDP and the anti-internal direct product of type 2 (AIDP-2). We rigorously investigate the properties of these two constructs, identifying the key conditions necessary for their existence and interaction. The culmination of our study is a significant theorem proving that within any UP (BCC)-algebra, a unique structure exists that simultaneously satisfies both the IDP and AIDP-2 concepts. This result opens new avenues for deeper exploration of algebraic structures and their applications.