Generators of projective MV-algebras

TL;DR

This paper characterizes the generators of projective MV-algebras, providing necessary and sufficient conditions, and introduces effective methods to identify such generators in bigenerated cases.

Contribution

It generalizes previous results by establishing a comprehensive criterion for generators of projective MV-algebras and offers practical procedures for their identification.

Findings

Established a necessary and sufficient condition for generators of projective MV-algebras.

Provided classes of projective generators for bigenerated MV-algebras.

Developed effective elementary procedures to determine generators.

Abstract

In the last decade, interest in projective MV-algebras has grown greatly; see [1], [5] e [6]. In this paper we establish a necessary and sufficient condition for n elements of the free n-generator MV-algebra to generate a projective MV-algebra. This generalizes the characterization of the n free generators proved in [7]. Using this, some classes of projective generators for bigenerated MV-algebras, are given. In particular, some effective procedures to determine, by elementary methods, generators of projective MV-algebras are.