NONNIL-P-COHERENT RINGS AND NONNIL-PP-RINGS

被引：0

作者：

Kim, Hwankoo ^{[1
]}

Mahdou, Najib ^{[2
]}

Oubouhou, El houssaine ^{[2
]}

机构：

[1] Hoseo Univ, Div Comp Engn, Asan 31499, South Korea

[2] Univ SM Ben Abdellah Fez, Fac Sci & Technol Fez, Dept Math, Box 2202, Fes, Morocco

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2024年 / 61卷 / 05期

基金：

新加坡国家研究基金会;

关键词：

Phi-P-flat; nonnil-P-injective; & ccedil; b-PF-ring; nonnil-PP-ring; nonnil- P-coherent ring; P-coherent ring; FLAT MODULES;

D O I：

10.4134/BKMS.b230427

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

. Let R be a commutative ring with nonzero identity. An Rmodule M is said to be Phi-P-flat if, for any s E R \ Nil(R) and any x E M such that x = 0, we have x E (0 : s)M. An R-module M is said to be nonnil-P-injective if, for any a E R \ Nil(R), every homomorphism from Ra to M extends to a homomorphism from R to M. Then R is said to be a nonnil-P-coherent ring (resp., Phi-PF, nonnil-PP-ring) if, for any a E R \ Nil(R), Ra is a finitely presented (resp., flat, projective) module. In this paper, we study nonnil-P-coherent rings, Phi-PF-rings, and nonnilPP-rings using Phi-P-flat and nonnil-P-injective modules.

引用

页码：1223 / 1240

页数：18