Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields

Jorge Jimenez; María Luisa Serrano; Branimir Šešelja; Andreja Tepavčević

doi:10.3390/axioms12080757

Axioms (Aug 2023)

Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields

Jorge Jimenez,
María Luisa Serrano,
Branimir Šešelja,
Andreja Tepavčević

Affiliations

Jorge Jimenez: Department of Mathematics, University of Oviedo, 33007 Oviedo, Spain
María Luisa Serrano: Department of Mathematics, University of Oviedo, 33007 Oviedo, Spain
Branimir Šešelja: Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia
Andreja Tepavčević: Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia

DOI: https://doi.org/10.3390/axioms12080757
Journal volume & issue: Vol. 12, no. 8
p. 757

Abstract

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Omega rings (Ω-rings) (and other related structures) are lattice-valued structures (with Ω being the codomain lattice) defined on crisp algebras of the same type, with lattice-valued equality replacing the classical one. In this paper, Ω-ideals are introduced, and natural connections with Ω-congruences and homomorphisms are established. As an application, a framework of approximate solutions of systems of linear equations over Ω-fields is developed.

Published in Axioms

ISSN: 2075-1680 (Online)
Publisher: MDPI AG
Country of publisher: Switzerland
LCC subjects: Science: Mathematics
Website: http://www.mdpi.com/journal/axioms

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