A Note on Dimension Modules

被引：1

作者：

Lomp, Christian ^{[1
,2
]}

Puczylowski, Edmund ^{[3
]}

机构：

[1] Univ Porto, Fac Sci, Dept Math, P-4169007 Oporto, Portugal

[2] Univ Porto, Ctr Math, P-4169007 Oporto, Portugal

[3] Univ Warsaw, Inst Math, Warsaw, Poland

来源：

COMMUNICATIONS IN ALGEBRA | 2015年 / 43卷 / 06期

关键词：

Dimension formula; Infinite Goldie dimension; 16P60; 16P20; 15D15; 16D20; SUM;

D O I：

10.1080/00927872.2014.890725

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In [2] Camillo and Zelmanowitz stated that rings all whose modules are dimension modules are semisimple Artinian. It seem however that the proof in [2] contains a gap and applies to rings with finite Goldie dimension only. In this paper we show that the result indeed holds for all rings with a basis as well as for all commutative rings with Goldie dimension attained.

引用

页码：2267 / 2271

页数：5

共 7 条

[1]

CAMILLO V, 1978, COMMUN ALGEBRA, V6, P345, DOI 10.1080/00927877808822249

[2] DIMENSION MODULES [J].

CAMILLO, VP ;

ZELMANOWITZ, JM .

PACIFIC JOURNAL OF MATHEMATICS, 1980, 91 (02) :249-261

[3] INFINITE GOLDIE DIMENSIONS [J].

DAUNS, J ;

FUCHS, L .

JOURNAL OF ALGEBRA, 1988, 115 (02) :297-302

[4]

DELVALLE A, 1994, COMMUN ALGEBRA, V22, P1257

[5] DIMENSION MODULES AND MODULAR LATTICES [J].

Domagalska, P. ;

Puczylowski, E. R. .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2012, 11 (05)

[6]

SIERPINSKI W, 1928, MONATSHEFTE MATH PHY, V35, P239

[7]

Wiliams Neil H., 1977, COMBINATORIAL SET TH

← 1 →