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$σ$-matching and interchangeable structures on null-filiform associative algebras

Kobiljon Abdurasulov, Jobir Adashev, Feruza Toshtemirova

Abstract

We describe $σ$-matching, interchangeable and, as a consequence, totally compatible products on null-filiform associative algebras.

$σ$-matching and interchangeable structures on null-filiform associative algebras

Abstract

We describe -matching, interchangeable and, as a consequence, totally compatible products on null-filiform associative algebras.
Paper Structure (3 sections, 16 theorems, 76 equations)

This paper contains 3 sections, 16 theorems, 76 equations.

Table of Contents

  1. Preliminaries.
  2. id-matching, interchangeable and totally compatible structure on (mu_0n, .)
  3. (12)-matching structure on (mu_0n, .)

Key Result

Theorem 5

An arbitrary $n$-dimensional null-filiform associative algebra is isomorphic to the algebra: where $\{e_1, \dots, e_n\}$ is a basis of the algebra $\mu_0^n$ and the omitted products vanish.

Theorems & Definitions (33)

  • Definition 1
  • Definition 2
  • Definition 3
  • Remark 4
  • Theorem 5: MO
  • Theorem 6: aku
  • Lemma 7
  • proof
  • Theorem 8
  • proof
  • ...and 23 more