PURE PROJECTIVE AND PURE INJECTIVE MODULES OVER POLYNOMIAL RINGS

被引：0

作者：

Mao, Lixin ^{[1
]}

机构：

[1] Nanjing Inst Technol, Sch Math & Phys, Nanjing 211167, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2025年 / 62卷 / 02期

关键词：

Polynomial ring; pure projective module; pure injective module;

D O I：

10.4134/BKMS.b240205

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the purity of modules over polynomial rings. It is proven that (1) X is a pure projective left R-module if and only if T(X) is a pure projective left R[x]-module if and only if Z(X) is a pure projective left R[x]-module; (2) f : A-* N is a pure projective precover (resp., pure projective cover) in R-Mod if and only if Z(f) : Z(A)-* Z(N) is a pure projective precover (resp., pure projective cover) in R[x]-Mod. Also, we obtain dual results about pure injective modules.

引用

页码：527 / 540

页数：14

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