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Metric ideals and its Structures Autometrized Lattice Ordered Monoids

Tekalign Regasa Ashale, Girum Aklilu Abebe, Kolluru Venkateswarlu

Abstract

This paper introduces the concept of metric ideals in AL-monoids. We also examine the structure of AL-monoids and describe some of the properties of homomorphism and fundamentalisomorphism theorems.Additionaly we introduce and examine a direct product and subdirect products in AL-monoids.

Metric ideals and its Structures Autometrized Lattice Ordered Monoids

Abstract

This paper introduces the concept of metric ideals in AL-monoids. We also examine the structure of AL-monoids and describe some of the properties of homomorphism and fundamentalisomorphism theorems.Additionaly we introduce and examine a direct product and subdirect products in AL-monoids.
Paper Structure (7 sections, 36 theorems, 1 equation)

This paper contains 7 sections, 36 theorems, 1 equation.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Results
  4. Prime ideals in AL-monoids
  5. Spectra of AL-monoids
  6. Homomorphism of Ideals in AL-monoids.
  7. Direct product, subdirect product, and representablity of AL-monoids.

Key Result

Theorem 3.1

Any ideal $I$ of an AL-monoid is a convex sub-AL-monoid in the sense that

Theorems & Definitions (55)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 3.1
  • Theorem 3.1
  • Definition 3.2
  • Remark 1
  • Remark 2
  • Theorem 3.2
  • ...and 45 more