Mathematical Structures defined by Identities III

TL;DR

This paper extends the formal theory of algebras with a single binary operation to include algebras with multiple operations of any arity, broadening the mathematical framework.

Contribution

It introduces a generalized framework for algebras with multiple operations of arbitrary arity, building on previous work with a single binary operation.

Findings

Develops a formal theory for multi-operation algebras

Provides new algebraic identities for complex operations

Extends previous binary operation results to multi-operation contexts

Abstract

We extend the theory (formal part only} of algebras with one binary operation (our paper arXiv:math/0110333v1 [math.RA] 31 Oct 2001) to algebras with several operations of any arity.