Reducibility and irreducibility of monomial matrices over commutative rings

被引：0
|
作者：
Bondarenko, Vitaliy M. [1 ]
Bortos, Maria Yu. [2 ]
Dinis, Ruslana F. [3 ]
Tylyshchak, Alexander A. [4 ]
机构：
[1] Inst Math, Fereshchenkivsk 3, UA-01601 Kiev, Ukraine
[2] Uzhgorod Natl Univ, Fac Math, UA-88000 Uzhgorod, Ukraine
[3] Kyiv Natl Tras Sheychenko Univ, Fac Mech & Math, UA-01033 Kiev, Ukraine
[4] Uzhgorod Natl Univ, Fac Math, UA-88000 Uzhgorod, Ukraine
来源：
ALGEBRA & DISCRETE MATHEMATICS | 2013年 / 16卷 / 02期
关键词：
irreducible matrix; similarity; local ring; Jacobson radical;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let R be a local ring with nonzero Jacobson radical. We study monomial matrices over R of the form 0 ... 0 t(sn) ( t(s1) ... 0 0 ) , 3 vertical dots (SIC) 3 vertical dots 3 vertical dots 0 ... t(sn-1) 0 and give a criterion for such matrices to be reducible when, n <= 6, s1 . . . , sn epsilon{0,1} and the radical is a principal ideal with generator t. We also show that the criterion does not hold for n = 7.
引用
收藏
页码：171 / 187
页数：17
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