KRULL DIMENSION AND CLASSICAL KRULL DIMENSION OF MODULES

被引：9

作者：

Castro Perez, Jaime ^{[1
]}

Rios Montes, Jose ^{[2
]}

机构：

[1] Inst Tecnol & Estudios Super Monterrey, Dept Matemat, Tlalpan 14380, Mexico

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Area Invest Cient, Mexico City 04510, DF, Mexico

来源：

COMMUNICATIONS IN ALGEBRA | 2014年 / 42卷 / 07期

关键词：

Classical Krull dimension; Krull dimension; Prime submodules; Semiprime submodules; Torsion theory; 16S90; 16D50; 16P50; 16P70; INJECTIVE-MODULES; RINGS; PRERADICALS;

D O I：

10.1080/00927872.2013.781611

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the concept of prime submodule defined by Raggi et al. in [16], for MR-Mod we define the concept of classical Krull dimension relative to a hereditary torsion theory M-tors. We prove that if M is progenerator in sigma[M], M-tors such that M has -Krull dimension then cl.Kdim(M)k(M). Also we show that if M is noetherian, -fully bounded, progenerator of sigma[M], and M ?, then clKdim(M)=k(M).

引用

页码：3183 / 3204

页数：22

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