Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields
Omega rings (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula>-rings) (and other related structures) are la...
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| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/8/757 |
| _version_ | 1797585511108313088 |
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| author | Jorge Jimenez María Luisa Serrano Branimir Šešelja Andreja Tepavčević |
| author_facet | Jorge Jimenez María Luisa Serrano Branimir Šešelja Andreja Tepavčević |
| author_sort | Jorge Jimenez |
| collection | DOAJ |
| description | Omega rings (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula>-rings) (and other related structures) are lattice-valued structures (with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula> being the codomain lattice) defined on crisp algebras of the same type, with lattice-valued equality replacing the classical one. In this paper, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula>-ideals are introduced, and natural connections with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula>-congruences and homomorphisms are established. As an application, a framework of approximate solutions of systems of linear equations over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula>-fields is developed. |
| first_indexed | 2024-03-11T00:07:08Z |
| format | Article |
| id | doaj.art-130d9f96d0f7481b9912c30b04818f09 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T00:07:08Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-130d9f96d0f7481b9912c30b04818f092023-11-19T00:14:47ZengMDPI AGAxioms2075-16802023-08-0112875710.3390/axioms12080757Omega Ideals in Omega Rings and Systems of Linear Equations over Omega FieldsJorge Jimenez0María Luisa Serrano1Branimir Šešelja2Andreja Tepavčević3Department of Mathematics, University of Oviedo, 33007 Oviedo, SpainDepartment of Mathematics, University of Oviedo, 33007 Oviedo, SpainDepartment of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, SerbiaDepartment of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, SerbiaOmega rings (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula>-rings) (and other related structures) are lattice-valued structures (with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula> being the codomain lattice) defined on crisp algebras of the same type, with lattice-valued equality replacing the classical one. In this paper, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula>-ideals are introduced, and natural connections with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula>-congruences and homomorphisms are established. As an application, a framework of approximate solutions of systems of linear equations over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Ω</mi></semantics></math></inline-formula>-fields is developed.https://www.mdpi.com/2075-1680/12/8/757fuzzy algebraomega ringfuzzy congruencefuzzy equalityideals in ringsomega fields |
| spellingShingle | Jorge Jimenez María Luisa Serrano Branimir Šešelja Andreja Tepavčević Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields Axioms fuzzy algebra omega ring fuzzy congruence fuzzy equality ideals in rings omega fields |
| title | Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields |
| title_full | Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields |
| title_fullStr | Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields |
| title_full_unstemmed | Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields |
| title_short | Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields |
| title_sort | omega ideals in omega rings and systems of linear equations over omega fields |
| topic | fuzzy algebra omega ring fuzzy congruence fuzzy equality ideals in rings omega fields |
| url | https://www.mdpi.com/2075-1680/12/8/757 |
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