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Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras

H. Ahmed

Department of Mathematics, Faculty of Science, Taiz University, Taiz, Yemen

Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Serdang, Selangor, Malaysia

E-mail Address: houida_m7@yahoo.com

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U. Bekbaev

Department of Natural and Mathematical Sciences, Turin Polytechnic University in Tashkent (TTPU), Tashkent, Uzbekistan

E-mail Address: uralbekbaev@gmail.com

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I. Rakhimov

Department of Mathematics, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), Shah Alam, Malaysia

V. I. Romanovski, Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

E-mail Address: isamiddin@uitm.edu.my

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https://doi.org/10.1142/S0218196720500253Cited by:4 (Source: Crossref)

Abstract

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.

Communicated by I. Shestakov

Keywords:

AMSC: 15A72, 16D25, 17A30, 17A99

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