Revisiting Baer elements

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. 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.

Keywords

• Multiplicative lattice
• compact element
• annihilator element
• Baer element
• Baer closure

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