Non-commutative finite associative algebras of 2-dimensional vectors
In this paper properties of the non-commutative finite associative algebra of two-dimensional vectors are presented. Interesting features of algebra are mutual associativity of all modifications of the defined parameterized multiplication operation and existing of a large set of single-side unit el...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vladimir Andrunachievici Institute of Mathematics and Computer Science
2017-12-01
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| Series: | Computer Science Journal of Moldova |
| Subjects: | |
| Online Access: | http://www.math.md/files/csjm/v25-n3/v25-n2-(pp344-356).pdf |
| _version_ | 1811263604044857344 |
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| author | Alexander Moldovyan Nicolay Moldovyan Victor Shcherbacov |
| author_facet | Alexander Moldovyan Nicolay Moldovyan Victor Shcherbacov |
| author_sort | Alexander Moldovyan |
| collection | DOAJ |
| description | In this paper properties of the non-commutative finite associative algebra of two-dimensional vectors are presented. Interesting features of algebra are mutual associativity of all modifications of the defined parameterized multiplication operation and existing of a large set of single-side unit elements. In the ordinary case one unique two-side unit element is connected with each element of the algebra, except the elements that are square roots from zero element. There are also presented four different variants of defining commutative associative algebras of 2-dimension vectors. For the case of commutativity the algebra has common unit element for all its elements. |
| first_indexed | 2024-04-12T19:48:24Z |
| format | Article |
| id | doaj.art-2711a26c273d48d28bd3f39f3a225899 |
| institution | Directory Open Access Journal |
| issn | 1561-4042 |
| language | English |
| last_indexed | 2024-04-12T19:48:24Z |
| publishDate | 2017-12-01 |
| publisher | Vladimir Andrunachievici Institute of Mathematics and Computer Science |
| record_format | Article |
| series | Computer Science Journal of Moldova |
| spelling | doaj.art-2711a26c273d48d28bd3f39f3a2258992022-12-22T03:18:54ZengVladimir Andrunachievici Institute of Mathematics and Computer ScienceComputer Science Journal of Moldova1561-40422017-12-01253(75)344356Non-commutative finite associative algebras of 2-dimensional vectorsAlexander Moldovyan0Nicolay Moldovyan1Victor Shcherbacov2Professor, St. Petersburg ITMO UniversityHead of the laboratory, St. Petersburg Institute for Informatics and Automation of Russian Academy of SciencesPrincipal Researcher, Institute of Mathematics and Computer Science of\\ the Academy of Sciences of MoldovaIn this paper properties of the non-commutative finite associative algebra of two-dimensional vectors are presented. Interesting features of algebra are mutual associativity of all modifications of the defined parameterized multiplication operation and existing of a large set of single-side unit elements. In the ordinary case one unique two-side unit element is connected with each element of the algebra, except the elements that are square roots from zero element. There are also presented four different variants of defining commutative associative algebras of 2-dimension vectors. For the case of commutativity the algebra has common unit element for all its elements.http://www.math.md/files/csjm/v25-n3/v25-n2-(pp344-356).pdffinite algebraringGalois fieldvectorassociative multiplicationparameterized multiplicationcryptoscheme |
| spellingShingle | Alexander Moldovyan Nicolay Moldovyan Victor Shcherbacov Non-commutative finite associative algebras of 2-dimensional vectors Computer Science Journal of Moldova finite algebra ring Galois field vector associative multiplication parameterized multiplication cryptoscheme |
| title | Non-commutative finite associative algebras of 2-dimensional vectors |
| title_full | Non-commutative finite associative algebras of 2-dimensional vectors |
| title_fullStr | Non-commutative finite associative algebras of 2-dimensional vectors |
| title_full_unstemmed | Non-commutative finite associative algebras of 2-dimensional vectors |
| title_short | Non-commutative finite associative algebras of 2-dimensional vectors |
| title_sort | non commutative finite associative algebras of 2 dimensional vectors |
| topic | finite algebra ring Galois field vector associative multiplication parameterized multiplication cryptoscheme |
| url | http://www.math.md/files/csjm/v25-n3/v25-n2-(pp344-356).pdf |
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