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Review
. 2023 Jun 15;9(6):e17190.
doi: 10.1016/j.heliyon.2023.e17190. eCollection 2023 Jun.

Orthopseudorings and congruences on distributive lattice with dual weak complementation

Eman Ghareeb Rezk  1   2
Affiliations
Review

Orthopseudorings and congruences on distributive lattice with dual weak complementation

Eman Ghareeb Rezk. Heliyon. .

Abstract

In this article, the concept of weak annulet is defined on the distributive lattice with dual weak complementation (DDWCL). Properties of weak annulets are proved. The relationship between orthopseudoring and ortho-lattice of all weak annulets of DDWCL is demonstrated. Congruence relations, with respect to weak annulets on DDWCL (W-congruences), are established. The double-face algebraic structure of all weak annulets and all W-congruence is investigated.

Keywords: 06B10; 06C15; 06D05; 06E20; 06E75; Congruence relation; Distributive lattice; Dual weakly complemented lattice; Ortho-lattice; Orthopseudoring.

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Conflict of interest statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figures

Figure 1
Figure 1
Graphs of the DDWCL L, ortho-lattice of weak annulets Λ(L) and ortho-lattice of Glivenko congruence classes L/≑.
Figure 2
Figure 2
WCon⋔¯(L) is the ortho-lattice of W-congruence relations on the lattice L.
Figure 3
Figure 3
Graphs of the weakly normal lattice K, Boolean algebra of weak annulets Λ(K) and Boolean algebra of Glivenko congruence classes K/≑.
Figure 4
Figure 4
WCon⋔¯(K) is the Boolean algebra of W-congruence relations on the lattice K.
See this image and copyright information in PMC

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