THE EXTENSION OF ROTH THEOREM FOR MATRIX EQUATIONS OVER A RING

Authors
Citation
Lp. Huang et Jz. Liu, THE EXTENSION OF ROTH THEOREM FOR MATRIX EQUATIONS OVER A RING, Linear algebra and its applications, 259, 1997, pp. 229-235
Citations number
9
Categorie Soggetti
Mathematics,Mathematics
ISSN journal
00243795
Volume
259
Year of publication
1997
Pages
229 - 235
Database
ISI
SICI code
0024-3795(1997)259:<229:TEORTF>2.0.ZU;2-8
Abstract
This paper extends Roth's similarity theorem as follows: Let R be a ri ng with identity, B(lambda) = Sigma(i=0)(k)B(i) lambda(i) is an elemen t of R-mxq[lambda]. If either R is a division ring and A is an element of R-nxn is algebraic, or R is finitely generated as a module over it s center, then the matrix equation Sigma(i=0)(k)A(i)XB(i) = C over R h as a solution if and only if ((lambda I-A)(-C)(O)(B lambda)) congruent to ((lambda I-A)(O)(O)(B lambda)). (C) Elsevier Science Inc., 1997.