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TitleNoncommutative Gröbner Basis over a Divisible and Annihilable Ring
Author(s) Nafissatou Diarra, Djiby Sow
TypeArticle in Conference Proceedings
Abstract The main objective of this article is to study noncommutative Gröbner bases over a divisible and annihilable ring (D-A ring). Such rings were introduced by Deepak Kapur and Yongyang Cai, and an algorithm for computing Gröbner bases in the commutative case was also given. If $I$ is an ideal of the associative algebra $V<x_1,...,x_n>=V<X>$ with non-commuting variables $x_1,...,x_n$ over a valuation ring $V$, a method for computing a Gröbner basis of $I$ was proposed recently. This method solves the membership problem in $I$ but does not allow to compute in the quotient ring $V<X>/I$. We generalized the method of Kapur and Cai in the noncommutative case. Our method allows to compute in the quotient ring $D<X>/I$, where $D$ is a D-A ring. This new approach for Gröbner basis over a D-A ring can have some applications in cryptography such as the study of the public key cryptosystem NTRU in ZnŒiŒX hX2 1i where ZnŒi is a D-A rin
KeywordsNoncommutative Gröbner basis • D-A rings • Zero divisor • Standard representations • A-polynomial • Overlaprelations • AS-reduced
URL http://www.springer.com/series/10533
JournalNon-Associative and Non-Commutative Algebra and Operator Theory
PublisherSpringer Proceedings in Mathematics & Statistics
Translation No
Refereed No
Institution Cheikh Anta Diop University