Pakistan Research Repository

standard Bases and Primary Decomposition in Polynomial Ring with Coefficients in Rings

Sadiq, Afshan (2011) standard Bases and Primary Decomposition in Polynomial Ring with Coefficients in Rings. PhD thesis, Govt. College University, Lahore.

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Abstract

The theory of standard bases in polynomial rings with coe cients 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 coe cients in Euclidean rings is given.This algorithm computes successively a Grobner basis replacing the reduction of one single s-polynomial in Buchberger's algorithm by the simultaneous reduction of several polynomials. And nally 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 nite elds, 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.

Item Type:Thesis (PhD)
Uncontrolled Keywords:Bases, Standard, Singular, Polynomial, Rings, Decomposition, Coefficients, Primary, Reduction, Algorithm
Subjects:Physical Sciences (f) > Mathematics(f5)
ID Code:6001
Deposited By:Mr. Javed Memon
Deposited On:18 Apr 2011 12:51
Last Modified:17 Aug 2011 10:30

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