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Mutations of $\mathfrak{perm}$ algebras

Ivan Kaygorodov, Farukh Mashurov

Abstract

We describe mutation elements in free $\mathfrak{perm}$ algebras. Moreover, we construct a base of free mutation of free $\mathfrak{perm}$ algebra. Using Cohn's criterion for the specialty of algebras, we show that there is an exceptional homomorphic image of mutation of free $\mathfrak{perm}$ algebras.

Mutations of $\mathfrak{perm}$ algebras

Abstract

We describe mutation elements in free algebras. Moreover, we construct a base of free mutation of free algebra. Using Cohn's criterion for the specialty of algebras, we show that there is an exceptional homomorphic image of mutation of free algebras.

Paper Structure

This paper contains 7 sections, 14 theorems, 43 equations.

Table of Contents

  1. Introduction
  2. $(p,q)$-mutations of $\mathfrak{perm}$ algebras
  3. Mutation elements in a free $\mathfrak{perm}$ algebra
  4. Mutation product of elements of the set $B$
  5. Identities in mutations of $\mathfrak{perm}$ algebras
  6. Homomorphic image of mutations of $\mathfrak{perm}$ algebras
  7. Open question

Key Result

Proposition 1

Let $x_1 , x_2 , x_3 \in P_{p,q}( X),$ then

Theorems & Definitions (25)

  • Proposition 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Theorem 5
  • proof
  • Lemma 6
  • ...and 15 more