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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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 2181967 |
| DOI: | 10.1142/S0218196720500253 |