Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems
This paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semanti...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/4/341 |
| _version_ | 1797606437532205056 |
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| author | Florin F. Nichita |
| author_facet | Florin F. Nichita |
| author_sort | Florin F. Nichita |
| collection | DOAJ |
| description | This paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>E</mi><mrow><mo> </mo><mi>I</mi><mo> </mo><mi>π</mi></mrow></msup><mo>+</mo><mi>U</mi><mo>=</mo><mi>O</mi></mrow></semantics></math></inline-formula>. We refer to a related equation, the Yang–Baxter equation, and to Yang–Baxter systems. The most consistent part of the paper is on the unification of rings and Boolean algebras. These new structures are related to the Yang–Baxter equation and to Yang–Baxter systems. |
| first_indexed | 2024-03-11T05:15:11Z |
| format | Article |
| id | doaj.art-8c55107497db4843957c280d1a2400cd |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T05:15:11Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-8c55107497db4843957c280d1a2400cd2023-11-17T18:19:03ZengMDPI AGAxioms2075-16802023-03-0112434110.3390/axioms12040341Unification Theories: Rings, Boolean Algebras and Yang–Baxter SystemsFlorin F. Nichita0Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, RomaniaThis paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>E</mi><mrow><mo> </mo><mi>I</mi><mo> </mo><mi>π</mi></mrow></msup><mo>+</mo><mi>U</mi><mo>=</mo><mi>O</mi></mrow></semantics></math></inline-formula>. We refer to a related equation, the Yang–Baxter equation, and to Yang–Baxter systems. The most consistent part of the paper is on the unification of rings and Boolean algebras. These new structures are related to the Yang–Baxter equation and to Yang–Baxter systems.https://www.mdpi.com/2075-1680/12/4/341Euler’s relationYang–Baxter equationringsBoolean algebras |
| spellingShingle | Florin F. Nichita Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems Axioms Euler’s relation Yang–Baxter equation rings Boolean algebras |
| title | Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems |
| title_full | Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems |
| title_fullStr | Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems |
| title_full_unstemmed | Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems |
| title_short | Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems |
| title_sort | unification theories rings boolean algebras and yang baxter systems |
| topic | Euler’s relation Yang–Baxter equation rings Boolean algebras |
| url | https://www.mdpi.com/2075-1680/12/4/341 |
| work_keys_str_mv | AT florinfnichita unificationtheoriesringsbooleanalgebrasandyangbaxtersystems |