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Topological insights into Monoids and Module systems

Doniyor Yazdonov, Carmelo Antonio Finocchiaro

Abstract

In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.

Topological insights into Monoids and Module systems

Abstract

In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.
Paper Structure (9 sections, 72 equations)

This paper contains 9 sections, 72 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Ideal systems
  4. Semistar operations
  5. The generalized $H$-module systems.
  6. Topology.
  7. On some generalizations; from Rings to Monoids
  8. The Zariski topology on the set of all $H$-module systems
  9. A characterization result

Theorems & Definitions (13)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • ...and 3 more