Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras
All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classifications of algebras with given number of subalgebras, left(right) ideals are provided. In particular, a list of isomorphism classes of all simple two-dimensional algebras is given...
| Published in: | International Journal of Algebra and Computation |
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| Format: | Article |
| Language: | English |
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World Scientific
2020
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| Online Access: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85082437163&doi=10.1142%2fS0218196720500253&partnerID=40&md5=6264cd45069d719b49aa4078a8f5499f |
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2-s2.0-85082437163 Ahmed H.; Bekbaev U.; Rakhimov I. Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras 2020 International Journal of Algebra and Computation 30 5 10.1142/S0218196720500253 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85082437163&doi=10.1142%2fS0218196720500253&partnerID=40&md5=6264cd45069d719b49aa4078a8f5499f All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classifications of algebras with given number of subalgebras, left(right) ideals are provided. In particular, a list of isomorphism classes of all simple two-dimensional algebras is given. In the study of ideals and subalgebras, the number of them depends on roots of certain system of polynomials at structure constants of the algebra. We also give explicit forms of the polynomials. © 2020 Oxford University Press. All rights reserved. World Scientific 2181967 English Article All Open Access; Green Open Access |
| author |
Ahmed H.; Bekbaev U.; Rakhimov I. |
| spellingShingle |
Ahmed H.; Bekbaev U.; Rakhimov I. Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras |
| author_facet |
Ahmed H.; Bekbaev U.; Rakhimov I. |
| author_sort |
Ahmed H.; Bekbaev U.; Rakhimov I. |
| title |
Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras |
| title_short |
Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras |
| title_full |
Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras |
| title_fullStr |
Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras |
| title_full_unstemmed |
Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras |
| title_sort |
Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras |
| publishDate |
2020 |
| container_title |
International Journal of Algebra and Computation |
| container_volume |
30 |
| container_issue |
5 |
| doi_str_mv |
10.1142/S0218196720500253 |
| url |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85082437163&doi=10.1142%2fS0218196720500253&partnerID=40&md5=6264cd45069d719b49aa4078a8f5499f |
| description |
All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classifications of algebras with given number of subalgebras, left(right) ideals are provided. In particular, a list of isomorphism classes of all simple two-dimensional algebras is given. In the study of ideals and subalgebras, the number of them depends on roots of certain system of polynomials at structure constants of the algebra. We also give explicit forms of the polynomials. © 2020 Oxford University Press. All rights reserved. |
| publisher |
World Scientific |
| issn |
2181967 |
| language |
English |
| format |
Article |
| accesstype |
All Open Access; Green Open Access |
| record_format |
scopus |
| collection |
Scopus |
| _version_ |
1809677897224421376 |