A Study of Tate Homology via the Approximation Theory with Applications to the Depth Formula
A Study of Tate Homology via the Approximation Theory with Applications to the Depth Formula
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DOI：
10.1007/s10114-023-1190-2
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发表时间：
2019-03
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影响因子：
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通讯作者：
Olgur Celikbas;L. Liang;A. Sadeghi;Tirdad Sharif
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文献类型：
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作者：
Olgur Celikbas;L. Liang;A. Sadeghi;Tirdad Sharif
本文主要讨论绝对模、相对模和Tate Tor模。本文的第一部分利用Auslander-Buchweitz逼近理论推广了Avramov和Martsinkovsky的一个结果，得到了绝对Tor模与相对Tor模和Tate Tor模之间的一个新的正合序列.在本文的第二部分中，我们考虑一个深度相等，称为深度公式，这已最初介绍了Auslander和进一步发展的Huneke和Wiegand。作为主要结果的应用，我们推广了Yassemi的一个结果，给出了有限Gorenstein模和有限内射维数模的深度公式成立的一个新的充分条件.
In this paper we are concerned with absolute, relative and Tate Tor modules. In the first part of the paper we generalize a result of Avramov and Martsinkovsky by using the Auslander—Buchweitz approximation theory, and obtain a new exact sequence connecting absolute Tor modules with relative and Tate Tor modules. In the second part of the paper we consider a depth equality, called the depth formula, which has been initially introduced by Auslander and developed further by Huneke and Wiegand. As an application of our main result, we generalize a result of Yassemi and give a new sufficient condition implying the depth formula to hold for modules of finite Gorenstein and finite injective dimension.