Mathematical Sciences: Conference on Computational Algebra -May 1992

Groebner基理论是交换环论和非对易环论计算工具发展的理论基础。在交换代数和代数几何方面已经取得了重要的成果，包括多项式因式分解和多项式的最大公约数的计算算法。有关于理想的初等分解、射影分解和合集的构造、理想的余维、Poincare和Hilbert级数以及确定理想隶属度的算法。对于非对易环，Groebner基正变得越来越重要。这里有复杂性，因为自由代数和路代数通常不是Notherian的。最近，已经设计了用于寻找合子、理想隶属度和计算Cartan行列式的算法。这一理论本身引发了关于算法及其作为程序实现的有趣问题。关于终止和有效性的理论问题正在研究中。该项目将支持将于1992年5月在乔治梅森大学举行的计算代数会议。会议将集中讨论计算代数的一些理论和实际应用，包括利用Groebner基的交换和非交换环论的主题，以及在其他领域的应用。

The theory of Groebner bases is the underlying theoretical base of the computational tools being developed in commutative and noncommutative ring theory. Important results have been achieved in commutative algebra and algebraic geometry, including algorithms for polynomial factorization and computation of the greatest common divisor of polynomials. There are algorithms for the primary decomposition of an ideal, the construction of projective resolutions and syzygies, the codimension of an ideal, the Poincare and Hilbert series, and the determination of ideal membership. For noncommutative rings, Groebner bases are becoming increasingly relevant. There are complications here since free algebras and path algebras are not Noetherian in general. Recently, algorithms have been designed for finding syzygies, ideal membership, and computation of the Cartan determinant. The theory itself has led to interesting questions about algorithms and their implementations as programs. Theoretical questions on termination as well as effectiveness are being studied. This project will support a Conference on Computational Algebra to be held in May 1992 at George Mason University. The conference will focus on some theoretical and practical applications of computational algebra, including topics in commutative and noncommutative ring theory which utilize Groebner bases, as well as applications to other fields.