KLI

Characterization of Radical in a Left Artinian Ring

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Alternative Title
좌 Artin환에서의 라디칼의 특성
Abstract
본 논문에서는 R을 좌 Artin환, N을 Jacobson 라디칼 이라할때 좌 R-module C가 단순 R-submodule의 직화로 표시되기 위한 필요하고도 충분한 조건은 NC=0임을 보인다.

그리고 더욱 나아가서 R-module ?A에서 R-module ?B로 가는 모든 R-module 준동형의 집합은 하나의 R-module이 될 수 있는데 이것이 R/N-module A/NA에서 R/N-module C로 가는 모든 R/N-module 준동형의 집합과 동형임을 밝힌다.
It is shown that a left R-module C can be represented as a direct sum of simple R-submodules if and only if NC=0, where R is left Artinian, and N is the Jacobson radical of R. Furthermore, it is proved that if R is a left Artinian ring, N the radical of R, and NC=0, then Hom?(A,C)?Hom???(A/N A, C), where Hom? (A, C) is the set of all R-module homomorphisms of an R-module ?A to ?B.
It is shown that a left R-module C can be represented as a direct sum of simple R-submodules if and only if NC=0, where R is left Artinian, and N is the Jacobson radical of R. Furthermore, it is proved that if R is a left Artinian ring, N the radical of R, and NC=0, then Hom?(A,C)?Hom???(A/N A, C), where Hom? (A, C) is the set of all R-module homomorphisms of an R-module ?A to ?B.
Author(s)
Lee,Kwang Yung
Issued Date
1970
Type
Research Laboratory
URI
https://oak.ulsan.ac.kr/handle/2021.oak/4930
http://ulsan.dcollection.net/jsp/common/DcLoOrgPer.jsp?sItemId=000002025256
Alternative Author(s)
이광영
Publisher
연구논문집
Language
eng
Rights
울산대학교 저작물은 저작권에 의해 보호받습니다.
Citation Volume
1
Citation Number
1
Citation Start Page
13
Citation End Page
15
Appears in Collections:
Research Laboratory > University of Ulsan Report
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