On identities in centrally nilpotent Moufang loops and centrally nilpotent A-loops

TL;DR

This paper proves that the variety generated by centrally nilpotent Moufang loops and A-loops is finitely based, contributing to the understanding of their algebraic structure.

Contribution

It establishes the finite basis property for the variety generated by centrally nilpotent Moufang loops and A-loops, a new result in loop theory.

Findings

Variety generated by these loops is finitely based.

Provides foundational results for algebraic identities in these loops.

Advances the theory of centrally nilpotent loops.

Abstract

This paper proves that the variety generated by a centrally nilpotent Moufang loop (or centrally nilpotent A-loop) is finitely based.