Groebner Basis And Its Applications

In this thesis we present the basic concepts and results of Groebner basis for a polynomialrnideal over a field and introduce an algorithm for computing and then present anrnimprovement of Buchberger's algorithms for computing Groebner basis by reducingrnnumber of S-polynomials without computing them. This paper deals with Groebnerrnbasis for a polynomial ideal over a ring by defining the module of a solution of arnhomogenous linear equation with polynomial coeffcients (called the syzygy module).rnAnd finally, we will see the application of Groebner basis in detail.

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