Computational ideal theory in finitely generated extension rings
Reads0
Chats0
TLDR
In this paper, the authors introduce natural graded structures of finitely generated extension rings and present subclasses of such structures which allow uniform algorithmic solutions of the basic problems in the associated graded ring and, hence, of the computation of Grobner bases with respect to the graded structure.About:
This article is published in Theoretical Computer Science.The article was published on 2000-08-06 and is currently open access. It has received 40 citations till now. The article focuses on the topics: Polynomial ring & Gröbner basis.read more
Citations
More filters
Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation
TL;DR: In this article, the authors studied the ring-theoretic properties of non-commutative polynomial algebras and proposed algorithms for computing the preimage of a left ideal.
Book
Solving Polynomial Equation Systems I
TL;DR: Mora as mentioned in this paper extended Buchberger's algorithm to group rings and other Ore-like extensions, and provided an operative scheme that allows one to set a Buchberger theory over any effective associative ring.
Book
Cited References
TL;DR: Transliteration of Russian names has essentially followed the system adopted by the Library of Congress, but with no distinction between e and e or between Η and fi, and with yu used for κ> and ya for H .
Journal ArticleDOI
Letterplace ideals and non-commutative Gröbner bases
TL;DR: A new method for computing non-commutative homogeneous Grobner bases via polynomials in commuting variables via letterplace analogues of graded two-sided ideals, which results in an example of a Buchberger procedure ''reduced by symmetry''.
Journal ArticleDOI
Differential Algebra for Derivations with Nontrivial Commutation Rules
TL;DR: In this paper, the authors consider the case where the derivations satisfy nontrivial commutation rules and develop the algebraic foundations for such a situation, which leads to algorithms for completion to formal integrability and differential elimination.
References
More filters
Journal ArticleDOI
Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: II
Book
Gröbner Bases: A Computational Approach to Commutative Algebra
TL;DR: This chapter discusses linear algebra in Residue Class Rings in Vector Spaces and Modules, and first applications of Gr bner Bases.
Book
An Introduction to Gröbner Bases
TL;DR: In this paper, the basic theory of Grobner bases is presented and a well-ordering and induction algorithm for well-ordered Grobners over rings is presented, along with a list of symbols.
Journal ArticleDOI
Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors
Journal ArticleDOI
Non-commutative Gröbner bases in algebras of solvable type
TL;DR: It is shown that reduced one- and two-sided Grobner bases in solvable polynomial rings are unique, and the word problem and the ideal membership problem for algebras of solvable type are solved, in particular in Clifford alge bras.