ROTHS THEOREMS OVER COMMUTATIVE RINGS

被引：36

作者：

GUSTAFSON, WH

机构：

[1] Department of Mathematics Texas Tech University Lubbock

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1979年 / 23卷 / FEB期

关键词：

D O I：

10.1016/0024-3795(79)90106-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1952, W.E. Roth showed that matrix equations of the forms AX-YB = C and AX-XB = C over fields can be solved if and only if certain block matrices built from A, B, and C are equivalent or similar. We show here that these criteria remain valid over arbitrary commutative rings. To do this, we use standard commutative algebra methods to reduce to the case of Artinian rings, where a simple argument with. © 1979.

引用

页码：245 / 251

页数：7

共 7 条

[1]

[Anonymous], ELEMENTS MATH ALGEBR

[2]

BOURBAKI N, 1961, ELEMENTS MATHEMATIQU, pCH3

[3] EQUIVALENCE OF PARTITIONED MATRICES [J].

FEINBERG, RB .

JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS SECTION B-MATHEMATICAL SCIENCES, 1976, 80 (01) :89-97

[4] SIMILARITY OF PARTITIONED MATRICES [J].

FEINBERG, RB .

JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS SECTION B-MATHEMATICAL SCIENCES, 1975, 79 (3-4) :117-125

[5]

GUSTAFSON WH, UNPUBLISHED

[6] ROTHS EQUIVALENCE PROBLEM IN UNIT REGULAR RINGS [J].

HARTWIG, RE .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 59 (01) :39-44

[7] THE EQUATIONS AX-YB=C AND AX-XB=C IN MATRICES [J].

ROTH, WE .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 3 (03) :392-396

← 1 →