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Revisiting Baer elements

Amartya Goswami, Themba Dube

Abstract

The objective of this paper is to extend certain properties observed in $d$-ideals of rings and $d$-elements of frames to Baer elements in multiplicative lattices introduced in D. D. Anderson, C. Jayaram, and P. A. Phiri, Baer lattices, \textit{Acta Sci. Math. (Szeged)}, 59 (1994), 61--74. Additionally, we present results concerning these elements that have not been addressed in the study of $d$-ideals of rings. Furthermore, we introduce Baer closures and explore Baer maximal, prime, semiprime, and meet-irreducible elements.

Revisiting Baer elements

Abstract

The objective of this paper is to extend certain properties observed in -ideals of rings and -elements of frames to Baer elements in multiplicative lattices introduced in D. D. Anderson, C. Jayaram, and P. A. Phiri, Baer lattices, \textit{Acta Sci. Math. (Szeged)}, 59 (1994), 61--74. Additionally, we present results concerning these elements that have not been addressed in the study of -ideals of rings. Furthermore, we introduce Baer closures and explore Baer maximal, prime, semiprime, and meet-irreducible elements.
Paper Structure (1 section, 25 theorems, 29 equations)

This paper contains 1 section, 25 theorems, 29 equations.

Table of Contents

  1. Declarations

Key Result

Lemma 1

In a multiplicative lattice $L$, the following hold.

Theorems & Definitions (51)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Proposition 4
  • proof
  • Proposition 5
  • proof
  • Proposition 6
  • proof
  • Remark 7
  • ...and 41 more