ID | 33679 |
FullText URL | |
Author |
Yi, Okyeon
|
Abstract | First, injective modules are one of the most popular objects in homological algebra. In most cases, base rings are commutative and Noetherian so that the testing the injectivity of a given module is an important topic. Bear's criterion for injective modules over any ring gives a big tool to classify injective modules. Every morphism from an ideal I of R should be extended to the whole ring R to be an injective module R-module. In this paper, we can show that the Baer's test can be reduced from all ideals of R to all prime ideals of R to test the injectivity of a given R-module M if the base ring R is commutative and Noetherian. Second, the Enochs' Theorem can be extended to an arbitrary sequence {ƒi} of endomomorphisms of an injective left Noetherian and if a diagram of the minimal injective resolution of RM is commutative, then the locally nilpotence of ƒ implies the locally nilpotence of other maps in the diagram. |
Keywords | Locally Nilpotent Endomorphism
Injective Modules
Injective Envelope
|
Published Date | 1998-01
|
Publication Title |
Mathematical Journal of Okayama University
|
Volume | volume40
|
Issue | issue1
|
Publisher | Department of Mathematics, Faculty of Science, Okayama University
|
Start Page | 7
|
End Page | 13
|
ISSN | 0030-1566
|
NCID | AA00723502
|
Content Type |
Journal Article
|
language |
English
|
File Version | publisher
|
Refereed |
True
|
NAID | |
Submission Path | mjou/vol40/iss1/2
|
JaLCDOI |