Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras
H. AhmedDepartment of Mathematics, Faculty of Science, Taiz University, Taiz, YemenUral BekbaevDepartment of Natural and Mathematical Sciences, Turin Polytechnic University in Tashkent (TTPU), Tashkent, UzbekistanI. S. RakhimovDepartment of Mathematics, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), Shah Alam, Malaysia
ABI
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.
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