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March 7, 2026Asian-European Journal of Mathematics0 citations

Compatible Relatively dual weakly complemented lattice

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ASArsham Borumand SaeidEREman Rezk

Key Points

  • The aim is to introduce and analyze the properties of relatively dual weakly complemented lattices, particularly focusing on compatibility and filters.
  • Defined relatively dual weakly complemented (RDWC) lattices within bounded lattices.
  • Investigated algebraic properties of RDWC and compatible RDWC lattices.
  • Studied relative closed and dense sets of elements.
  • Defined various types of filters on compatible RDWC lattices and explored their relationships.
  • Introduced the concept of compatible RDWC lattices and their defining characteristics.
  • Established relationships between different types of filters in compatible RDWC lattices.
  • Outlined the fundamental algebraic properties of the newly defined lattices.

Abstract

The concept of relatively dual weakly complementation on a bounded lattice is introduced. Also, relatively dual weakly complemented (RDWC) and compatible RDWC lattices are defined. Some of the algebraic properties are investigated. Relative closed and dense sets of elements are defined and studied. Finally, some types of filters are defined on a compatible RDWC lattice, and the conditional relationships between different types of filters are investigated.

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Cite This Study

Saeid et al. (2026) studied this question.

synapsesocial.com/papers/69abc1955af8044f7a4ea54fhttps://doi.org/10.1142/s1793557126500312
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