Noetherian rings of low global dimension and syzygetic prime ideals

Planas-Vilanova Francesc

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Noetherian rings of low global dimension and syzygetic prime ideals

机译：低全球维度和Syzygetic Prime的Neetherian戒指

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摘要

Let R be a Noetherian ring. We prove that R has global dimension at most two if, and only if, every prime ideal of R is of linear type. Similarly, we show that R has global dimension at most three if, and only if, every prime ideal of R is syzygetic. As a consequence, we derive a characterization of these rings using the Andre-Quillen homology. (C) 2020 Elsevier B.V. All rights reserved.

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《Journal of pure and applied algebra》 |2021年第2期|共8页
作者
Planas-Vilanova Francesc;
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作者单位

Univ Politecn Cataluna Dept Matemat ETSEIB Diagonal 647 E-08028 Barcelona Catalunya Spain;

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原文格式 PDF
正文语种 eng
中图分类代数、数论、组合理论;
关键词
Global dimension; Noetherian regular rings; Ideal of linear type; Syzygetic ideal;

机译：全球层面;Noetherian正则环;理想的线性类型;合子理想;

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5. On the ring of quotients at a prime ideal of a right noetherian ring [J] . A. G. Heinicke Canadian Journal of Mathematics . 1972,第1972期

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7. ON PRIME IDEALS OF NOETHERIAN SKEW POWER SERIES RINGS [J] . EDWARD S. LETZTER Israel Journal of Mathematics . 2012,第1期

机译：关于偏北偏功率系列环的主要概念
8. Projectively full ideals in Noetherian rings, a survey [C] . Catalin Ciuperca, William Heinzer, Jack Ratliff, International Conference on Midwest Algebra, Geometry and their Interactions . 2007

机译：调查中的Neetherian Rings的Projective完整的理想
9. Prime ideals in low-dimensional mixed polynomial/power series rings. [D] . Eubanks-Turner, Christina. 2008

机译：低维混合多项式/幂级数环的素理想。
10. HOMOLOGICAL DIMENSION IN NOETHERIAN RINGS [O] . Maurice Auslander, David A. Buchsbaum 1956

机译：努氏环中的同维数
11. Noetherian rings of low global dimension and syzygetic prime ideals [O] . Francesc Planas-Vilanova 2021

机译：低全球维度和Syzygetic Prime的Neetherian戒指
12. Complete Ideals in Regular Local Rings of Dimension 2. [R] . Oscar Zariski 1959

机译：维数2的正则局部环中的完备理想。

Noetherian rings of low global dimension and syzygetic prime ideals

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