平坦的多项式剩余类环

王芳贵

数学学报 ›› 2002, Vol. 45 ›› Issue (6) : 1171-117.

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PDF(384 KB)
数学学报 ›› 2002, Vol. 45 ›› Issue (6) : 1171-117. DOI: 10.12386/A2002sxxb0152
论文

平坦的多项式剩余类环

    王芳贵
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The Flat Residual Rings of Polynomials

    Fang Gui WANG
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摘要

本文证明了如果多项式的剩余类环 A=R[T]/fR[T]作为 R-模是平坦模,且R是约化环,则f是正规多项式.特别地,若R还是连通的,则f的首项系数是单位.也证明了弱整体有限的凝聚环是约化环,以及弱整体为有限的凝聚连通环是整环.

Abstract

Abstract In this note, we prove that if R is a reduced ring and A = R[T]/fR[T] is a finitely generated R-module, then f is a normal polynomial. Moreover, if R is connected, then the leading coefficient of / is a unit. It is also proved that a coherent connected ring with finite weak global dimension is a domain.

关键词

约化环 / 多项式 / 连通环 / 平坦模

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王芳贵. 平坦的多项式剩余类环. 数学学报, 2002, 45(6): 1171-117 https://doi.org/10.12386/A2002sxxb0152
Fang Gui WANG. The Flat Residual Rings of Polynomials. Acta Mathematica Sinica, Chinese Series, 2002, 45(6): 1171-117 https://doi.org/10.12386/A2002sxxb0152
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