Meiirbek K.2025-06-132025-06-132023Meiirbek K / Grobner-Shirshov bases theory for Zinbiel stperalgebras / 7M05401 - Department of Mathematics and Natural Sciences / 2023https://repository.sdu.edu.kz/handle/123456789/1758This thesis is a collection of 6 chapters .The Grébner-Shirshov basis is an impor- tant mathematical apparatus in algebra and commutative algebra, which is used to study and analyze polynomials and their ideals. The Grdébner-Shirshov basis has a number of important properties that make it a powerful tool for solving various algebraic problems, such as searching for ideals, solving systems of equa- tions and determining the basic invariants of polynomials. In this paper we will construct a Grobner-Shirshov basis for Zinbiel algebras. Algebra with the identity (ab) c = a(bc) + a(cb) is called the Zinbiel algebra. In the process of construct- ing the Grebner-Shirshov basis, two compositions are found and the composition lemma is proved. The method of mathematical induction is used to prove the lemma.enpolynomialsGrdébner-ShirshovalgebraThesis