On Gorenstein Homological Dimensions Over the Tensor Product of Algebras

IF 0.7 4区数学 Q2 MATHEMATICS Bulletin of The Iranian Mathematical Society Pub Date : 2024-09-06 DOI:10.1007/s41980-024-00912-w

Yueming Xiang

引用次数: 0

Abstract

Let k be a commutative ring, and let $\Lambda $ and $\Gamma $ be two k-algebras. In this paper, we give upper and lower bounds of Gorenstein global dimension and Gorenstein weak dimension over the tensor product $\Lambda \otimes _k \Gamma $. As its applications, the Gorenstein dimensions of several special algebras such as group algebras, matrix algebras, triangular matrix algebras and polynomial algebras can be computed. Moreover, we compare the Gorenstein global dimension of the enveloping algebra $\Lambda ^e$ of $\Lambda $ with the Gorenstein projective dimension of $\Lambda $. Some well-known results are also extended.

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论代数张量积上的戈伦斯坦同调维数

让 k 是交换环，让 $\Lambda $ 和 $\Gamma $ 是两个 k 矩阵。本文给出了张量积 $\Lambda \otimes _k \Gamma $上的 Gorenstein 全局维度和 Gorenstein 弱维度的上界和下界。作为其应用，我们可以计算几个特殊代数的戈伦斯坦维度，如群代数、矩阵代数、三角矩阵代数和多项式代数。此外，我们还比较了 $\Lambda $ 的包络代数 $\Lambda ^e$ 的戈伦斯坦全维度和 $\Lambda $ 的戈伦斯坦投影维度。一些著名的结果也得到了扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

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1.40

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0.00%

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期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.

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