A version of the baer splitting problem for noetherian rings

Cornelius Greither; Dolors Herbera; Jan Trlifaj

doi:10.1515/9783110203035.375

A version of the baer splitting problem for noetherian rings

Cornelius Greither, Dolors Herbera, Jan Trlifaj

Department of Mathematics

Research output: Chapter in Book › Chapter › Research › peer-review

Abstract

We call a module M over a commutative noetherian ring R quasi-Baer provided that Ext1 R(M,T) = 0 for each locally artinian (= semiartinian) module T. We prove that all quasi-Baer modules are projective in case R has finite Krull dimension, or R is of cardinality < אω. © de Gruyter 2008.

Original language	English
Title of host publication	Models, Modules and Abelian Groups: In Memory of A. L. S. Corner
Pages	375-383
Number of pages	8
DOIs	https://doi.org/10.1515/9783110203035.375
Publication status	Published - 10 Dec 2008

Keywords

Commutative noetherian rings
Locally artinian modules
Mittag-leffler modules
Quasi-Baer modules

Access to Document

10.1515/9783110203035.375

Cite this

@inbook{69801e651a5641bbad7fe0c5f1d705ba,

title = "A version of the baer splitting problem for noetherian rings",

abstract = "We call a module M over a commutative noetherian ring R quasi-Baer provided that Ext1 R(M,T) = 0 for each locally artinian (= semiartinian) module T. We prove that all quasi-Baer modules are projective in case R has finite Krull dimension, or R is of cardinality < אω. {\textcopyright} de Gruyter 2008.",

keywords = "Commutative noetherian rings, Locally artinian modules, Mittag-leffler modules, Quasi-Baer modules",

author = "Cornelius Greither and Dolors Herbera and Jan Trlifaj",

year = "2008",

month = dec,

day = "10",

doi = "10.1515/9783110203035.375",

language = "English",

isbn = "9783110194371",

pages = "375--383",

booktitle = "Models, Modules and Abelian Groups: In Memory of A. L. S. Corner",

}

TY - CHAP

T1 - A version of the baer splitting problem for noetherian rings

AU - Greither, Cornelius

AU - Herbera, Dolors

AU - Trlifaj, Jan

PY - 2008/12/10

Y1 - 2008/12/10

N2 - We call a module M over a commutative noetherian ring R quasi-Baer provided that Ext1 R(M,T) = 0 for each locally artinian (= semiartinian) module T. We prove that all quasi-Baer modules are projective in case R has finite Krull dimension, or R is of cardinality < אω. © de Gruyter 2008.

AB - We call a module M over a commutative noetherian ring R quasi-Baer provided that Ext1 R(M,T) = 0 for each locally artinian (= semiartinian) module T. We prove that all quasi-Baer modules are projective in case R has finite Krull dimension, or R is of cardinality < אω. © de Gruyter 2008.

KW - Commutative noetherian rings

KW - Locally artinian modules

KW - Mittag-leffler modules

KW - Quasi-Baer modules

U2 - 10.1515/9783110203035.375

DO - 10.1515/9783110203035.375

M3 - Chapter

SN - 9783110194371

SP - 375

EP - 383

BT - Models, Modules and Abelian Groups: In Memory of A. L. S. Corner

ER -

A version of the baer splitting problem for noetherian rings

Abstract

Keywords

Access to Document

Fingerprint

Cite this