DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in press

Authors:

S. El-Assar

Sanaa El-Assar

Departement of Mathematics, Faculty of Science, Tanta University

email: sanaa.elassar@science.tanta.edu.eg

0009-0003-0804-6222

A. Badawy

Abd El-Mohsen Mohamed Badawy

Tanta University Faculty of Sciences Math. Dept. Egypt

email: abdel-mohsen.mohamed@science.tanta.edu.eg

0000-0001-9995-4610

T. El-Sheikh

Tahany El-Sheikh

Department of Mathematics, Faculty of Science, Tanta University

email: tahany.elshaikh@science.tanta.edu.eg

E. Gomaa

Eman Gomaa

Department of Mathematics Faculty of Science,Tanta University, Egypt

email: eman.gomaa@science.tanta.edu.eg

0009-0008-7760-8600

Title:

$k$-ideals and $k$-$\{^+\}$-congruences of core regular double Stone algebras

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Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2023-08-15 , Revised: 2024-02-28 , Accepted: 2024-02-28 , Available online: 2025-02-18 , https://doi.org/10.7151/dmgaa.1472

Abstract:

In this paper, the authors study many interesting properties of ideals and congruences of the class of a core regular double Stone algebra (briefly $CRD$-Stone algebra). We introduce and characterize the concepts of $k$-ideals and principal $k$-ideals of a core regular double Stone algebra with the core element $k$ and establish the algebraic structures of such ideals. Also, we investigate $k$-$\{^+\}$-congruences and principal $k$-$\{^+\}$-congruences of a $CRD$-Stone algebra $L$ which are induced by $k$-ideals and principal $k$-ideals of $L$, respectively. We obtain an isomorphism between the lattice of $k$-ideals (principal $k$-ideals) and the lattice of $k$-$\{^+\}$-congruences (principal $k$-$\{^+\}$-congruences) of a $CRD$-Stone algebra. We provide some examples to clarify the basic results of this article.

Keywords:

Stone algebras, double Stone algebras, regular double Stone algebras, core regular double Stone algebras, ideals, filters

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