Cohen-Macaulay同调维数

Pub Date : 2019-04-07 DOI:10.7146/math.scand.a-119382

P. Sahandi, Tirdad Sharif, S. Yassemi

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引用次数: 3

摘要

我们引入了新的同调维数，即同调有界复合体的Cohen-Macaulay射影维数、内射维数和平面维数。除其他外，我们证明(a)这些不变量表征局部环的Cohen-Macaulay性质，(b) Cohen-Macaulay平面维数在Gorenstein平面维数和大受限平面维数之间的拟合，以及(c) Cohen-Macaulay内射维数在Gorenstein内射维数和Chouinard不变量之间的拟合。

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Cohen-Macaulay homological dimensions

We introduce new homological dimensions, namely the Cohen-Macaulay projective, injective and flat dimensions for homologically bounded complexes. Among other things we show that (a) these invariants characterize the Cohen-Macaulay property for local rings, (b) Cohen-Macaulay flat dimension fits between the Gorenstein flat dimension and the large restricted flat dimension, and (c) Cohen-Macaulay injective dimension fits between the Gorenstein injective dimension and the Chouinard invariant.

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