On the Chang's group of BL-algebras

TL;DR

This paper constructs an associated lattice Abelian group for any BL-algebra, generalizing Chang's group for MV-algebras, and explores its properties and examples.

Contribution

It introduces a new construction of an Abelian group linked to BL-algebras, extending Chang's group concept beyond MV-algebras.

Findings

The constructed group coincides with Chang's group for MV-algebras.

The Chang's group of the MV-center is a direct summand in the constructed group.

Examples of the constructed group are computed and analyzed.

Abstract

For an arbitrary BL-algebra L, we construct an associated lattice Abelian group that coincides with Chang's group when the BL-algebra is an MV-algebra. We prove that the Chang's group of the MV-center of any BL- algebra L is a direct summand in the above group. We also compute examples of this group.