Preprint

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

Hassan A. Al-Hadi AhmedDepart. of Math. , Faculty of Science , Taiz University , Taiz , Yemen &U. BekbaevDepartment of Math. , Faculty of Science , UPM , Selangor , MalaysiaI. RakhimovLaboratory of Cryptography, Analysis and Structure , Institute for Mathematical Research (INSPEM) , UPM , Serdang , Selangor , Malaysia

2018en

ABI

Annotatsiya

All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classification 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 depend on roots of certain system of polynomials at structure constants of the algebra. We also give explicit forms of the polynomials.

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Identifikatorlar

DOI: 10.48550/arxiv.1810.06780

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