Browsing by Author "Belete, Solomon"

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    Groebner Basis and its Applications
    (Addis Ababa University, 2012-06) Belete, Solomon; Bekele, Berhanu(PhD)
    In this thesis we present the basic concepts and results of Groebner basis for a polynomial ideal over a field and introduce an algorithm for computing and then present an improvement of Buchberger's algorithms for computing Groebner basis by reducing number of S-polynomials without computing them. This paper deals with Groebner basis for a polynomial ideal over a ring by defining the module of a solution of a homogenous linear equation with polynomial coeffcients (called the syzygy module). And finally, we will see the application of Groebner basis in detail.