Gröbner Bases Exist For Any Monomial Ordering, Gröbner Basis Is Termed Reduced If The Leading Coefficient Of Each Element Of The Basis Is 1 And No Monomial In Any Element Of The Basis Is In The Ideal Generated By The Leading Terms Of The Other Elements Of

Abstract

System studied is as follows: Gröbner Bases Exist For Any Monomial Ordering, Gröbner Basis Is Termed Reduced If The Leading Coefficient Of Each Element Of The Basis Is 1 And No Monomial In Any Element Of The Basis Is In The Ideal Generated By The Leading Terms Of The Other Elements Of The Basis, On Computing Krull Dimension Of Residue Class Polynomial Rings Over Integral Domains Using Gröbner Bases, Arbitrary Noetherian Rings, Hilbert Function Hilbert Series And Hilbert Polynomials, Theory And The Algorithms Of Gröbner Bases Of Modules To The Theory And The Algorithms Of Gröbner Bases Of Ideals, Concept And Algorithms Of Gröbner Bases Have Also Been Generalized To Ideals Over Various Rings, Commutative Or Not, Like Polynomial Rings Over A Principal Ideal Ring Or Weyl Algebras

The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-864130-870779.pdf