Matrix Rings over Reflexive Rings

被引：0
|
作者：
Cheon, Jeoung Soo [1 ]
Kwak, Tai Keun [2 ]
Lee, Yang [3 ]
机构：
[1] Pusan Natl Univ, Dept Math, Busan 46241, South Korea
[2] Daejin Univ, Dept Math, Pochon 11159, South Korea
[3] Daejin Univ, Inst Basic Sci, Pochon 11159, South Korea
来源：
ALGEBRA COLLOQUIUM | 2018年 / 25卷 / 03期
基金：
新加坡国家研究基金会;
关键词：
weakly reflexive ring; reflexive ring; power of ideal; matrix ring; ring of minimal order; REVERSIBLE RINGS; PROPERTY; IDEMPOTENTS; IDEALS;
D O I：
10.1142/S1005386718000317
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The concept of reflexive property is introduced by Mason. This note concerns a ring-theoretic property of matrix rings over reflexive rings. We introduce the concept of weakly reflexive rings as a generalization of reflexive rings. From any ring, we can construct weakly reflexive rings but not reflexive, using its lower nilradical. We study various useful properties of such rings in relation with ideals in matrix rings, showing that this new property is Morita invariant. We also investigate the weakly reflexive property of several sorts of ring extensions which have roles in ring theory.
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页码：459 / 474
页数：16
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