$\mathbb{N}$-分次可解多项式代数上极小分次自由分解的计算
环与代数
2015-06-22 v2
摘要
本文表明，在（A. Capani 等，Computing minimal finite free resolutions, {\it Journal of Pure and Applied Algebra}, (117& 118)(1997), 105 -- 117; M. Kreuzer 与 L. Robbiano, {\it Computational Commutative Algebra 2}, Springer, 2005.）中开发的用于计算交换多项式代数上自由模的分次子模与分次商模的极小齐次生成系的方法与算法，可以适用于计算加权 -分次可解多项式代数上自由模的分次子模与分次商模的极小齐次生成系，其中可解多项式代数的定义见（A. Kandri-Rody 与 V. Weispfenning, Non-commutative Gr"obner bases in algebras of solvable type. {\it J. Symbolic Comput.}, 9(1990), 1--26）。由此，实现了在加权 -分次可解多项式代数上计算极小有限分次自由分解的算法过程。
引用
@article{arxiv.1401.5206,
title = {Computation of Minimal Graded Free Resolutions over $\mathbb{N}$-Graded Solvable Polynomial Algebras},
author = {Huishi Li},
journal= {arXiv preprint arXiv:1401.5206},
year = {2015}
}
备注
25 pages. Introduction Section 1, Algorithm 2, Algorithm 3, and the last paragraph of the proof of Theorem 5.4 are revised; several new references are added. arXiv admin note: substantial text overlap with arXiv:1401.5464