Browsing by Author "Akhmetova Zh."

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    Variety of Bicommutative Algebra defined by identities
    (Faculty of Engineering and Natural Sciences, 2023) Akhmetova Zh.
    One of the key inquiries in modern algebra is the investigation of algebras that satisfy specific identities.Within the domain of polynomial identities we have 2 questions. The first is to describe an algebra by a defined identity. The second is to describe identities in algebra. The study of identities will help us in the construction of basis of free algebra, in the study of the Hilbert sequence, the Specht problem and problems of the finite basis. In this work, we used two differ- ent research methods. First, the theory of representations of symmetric groups. Second, the theory of representations of linear groups. In this research paper, we have completely described the subvariety of varirty of bicommutative alge- bras defined by the identities (ab)c + (ba)c + (ca)b + c(ba) + c(ab) + a(bc) = 0, 7[(ab)e — 2(ba)e + (ca)b] + d[e(ba) — 2c(ab) + a(bc)] = 0.