2. Theses and Dissertations

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Browsing 2. Theses and Dissertations by Subject "algebra"

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    Fujita hypothesis and birational models in algebraic geometry
    (Faculty of Engineering and Natural Sciences, 2019) Kunanbaev A.
    The aim of mv research is to study Fujita hypotheses. which states that if is a smooth projektive varvety of dimension n then: (i) Assume that XV. is.a minimal (i.c.. Ay is nef) varvety of general type.(ie., Ky is big == NY > 9). Then the linear system |nvAx| is free for m > n+ 2; (ii) Let A be an ample invertible sheaf on X. Then the linear system |mJvy + (n +1) Al is free. and JnKy + (n+ 2) Al is verv ample on Y, For surfaces Fujita hypotheses was proved by Igor Reider. In my work I generalize result for X not be a sinooth projektive varyety but F-rational. So if Fujita hypotheses is true for a smooth projektive varyety then it is true for more general case F-rational. I use methods of commutative algebra and definition of tight closure.
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    Grobner-Shirshov bases theory for Zinbiel stperalgebras
    (Faculty of Engineering and Natural Sciences, 2023) Meiirbek K.
    This 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.
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    Sn-MODULE STRUCTURES OF FREE ANTI-COMMUTATIVE ALGEBRA
    (Faculty of Engineering and Natural Science, 2024) Abdibek Y,
    An algebra with identity ab = −ba is called anti-commutative algebra. In this work we study Sn-module structures of free anti-commutative algebra of degree n.