Home > Search Results: keywords:"polynomial rings|ideals|Gröbner basis|Buchberger's algorithm|Standard basis|Syzygies of modules"
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Groebner bases
 Mašková, Kristýna ; Trlifaj, Jan (advisor) ; Příhoda, Pavel (referee)
Gröbner basis is a particular kind of a generating set of an ideal in the polynomial ring S = K[x1, . . . , xn]. This notion is based upon the concept of a monomial order. We define these concepts and present Buchberger's criterion, that enables us to effectively verify whether a generating set is a Gröbner basis. We introduce Buchberger's algorithm, that produces a Gröbner basis from a finite set of generators. We consider a special case of linear homogeneous ideals, where Gröbner basis can be computed simply by the Gaussian elimination. Finally, we extend this theory to submodules of free modules and briefly indicate how to use Gröbner bases to prove Hilbert's syzygy theorem. 1
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