Ore扩张剩余类环的忠实平坦性质
The Faithfully Flat Property of the Residue Rings of Ore Extension Rings
DOI: 10.12677/PM.2020.101003, PDF,   
作者: 龚朝庆, 欧阳伦群：湖南科技大学，数学与计算科学学院，湖南 湘潭
关键词: (α；δ)-相容理想；平坦模；忠实平坦模；(α；δ)-Compatible Ideal； Flat Module； Faithfully Flat Module
摘要: 设α是环R的自同构，δ是环R的α -导子，f(x)是Ore扩张环R[x;α,δ]中的一个斜多项式。通过讨论f(x)的系数与R[x;α,δ]/(f(x))的忠实平坦性质之间的关系，得到了R[x;α,δ]/(f(x))是忠实平坦R-模时应满足的几个充分条件。
Abstract: Let α be an automorphism and δ an α-derivation of a ring R, f(x) be a skew polynomial in the Ore extension ring R[x;α,δ]. We mainly investigate the relations between the coefficients of f(x) and the faithfully flat property of [x;α,δ]/(f(x)), and obtain some sufficient conditions for [x;α,δ]/(f(x)) being a faithfully flat R-module.
文章引用：龚朝庆, 欧阳伦群. Ore扩张剩余类环的忠实平坦性质[J]. 理论数学, 2020, 10(1): 11-16. https://doi.org/10.12677/PM.2020.101003

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