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Associative ideals in monoids

Volodymyr Zhuravlov

Abstract

The article investigates the properties of associative ideals in monoids. Such ideals have some applications in the logic of non-standard sequences and category theory. The relations of these ideals with the verbal structure of words over generators are examined. Finitely and infinitely generated monoids are treated separately.

Associative ideals in monoids

Abstract

The article investigates the properties of associative ideals in monoids. Such ideals have some applications in the logic of non-standard sequences and category theory. The relations of these ideals with the verbal structure of words over generators are examined. Finitely and infinitely generated monoids are treated separately.
Paper Structure (7 sections, 10 equations)

This paper contains 7 sections, 10 equations.

Table of Contents

  1. Introduction
  2. Properties of associative ideals
  3. The connection of associative and prime ideals with the Cartesian product of the set of generators
  4. On infinite divisibility
  5. Roots of monoids and quadratic monoids
  6. Logical Notes
  7. References