Ideal cotorsion pairs over one point extensions

IF 1 4区数学

Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2022-06-16 DOI:10.1007/s11766-022-4375-z

Hai-yan Zhu, Ben-jun Du, Qi-kai Wang

引用次数: 0

Abstract

Let R[P] be the one point extension of a k-algebra R by a projective R-module P. We prove that the extension of a complete ideal cotorsion pair in R-Mod is still a complete ideal cotorsion pair in R[P]-Mod. As an application, it is obtainable that the operation (−)_m [P] satisfies the so-called distributive law relating the operations of products and extensions of ideals under appropriate conditions.

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一点扩展上的理想扭转对

设R[P]是k-代数R通过投影R-模P的一点扩张。我们证明了R-Mod中完全理想余对的扩张仍然是R[P]-Mod中的完全理想余对数。作为一个应用，可以得到运算（−）m[P]在适当的条件下满足关于乘积的运算和理想的扩张的所谓分配律。

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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来源期刊

Applied Mathematics-A Journal of Chinese Universities Series B MATHEMATICS, APPLIED-

自引率

10.00%

发文量

期刊介绍： Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects. The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry. Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.