Please use this identifier to cite or link to this item:
Title: Standard Bases and Primary Decomposition in Polynomial Ring with Coefficients in Rings
Authors: Sadiq, Afshan
Keywords: Natural Sciences
Issue Date: 2006
Publisher: GC University Lahore, Pakistan
Abstract: The theory of standard bases in polynomial rings with coefficients in a ring A with respect to local orderings is developed. A is a commutative Noetherian ring with 1 and we assume that linear equations are solvable in A. Then the generalization of Faug ́ere F4-algorithm for polynomial rings with coefficients in Euclidean rings is given. This algorithm computes successively a Gr ̈obner basis replacing the reduction of one single s-polynomial in Buchberger’s algorithm by the simultaneous reduction of several polynomials. And finally we present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and the idea of Shimoyama–Yokoyama resp. Eisenbud–Hunecke–Vasconcelos to extract primary ideals from pseudo-primary ideals. A parallelized version of the algorithm is implemented in Singular.
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

Files in This Item:
File Description SizeFormat 
700S.pdfComplete Thesis371.21 kBAdobe PDFView/Open
700S-0.pdfTable of Contents43.82 kBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.