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The extension of Roth's theorem for matrix equations over a ring

✍ Scribed by Liping Huang; Jianzhou Liu

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
345 KB
Volume
259
Category
Article
ISSN
0024-3795

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✦ Synopsis

This paper extends Roth's similarity theorem as follows: Let R be a ring with identity, B(A) = CfZoBiA' E R mxq[ A]. If either R is a division ring and A E R,, ,, is algebraic, or R is finitely generated as a module over its center, then the matrix equation Et= o A"XB, = C over R has a solution if and only if

πŸ“œ SIMILAR VOLUMES

The Ring of Quotients of R[S]; R a Commu
The Ring of Quotients of R[S]; R a Commutative Ring and S a REES Matrix Semigroup over a Semigroup
✍ James A. Bate; John K. Luedeman πŸ“‚ Article πŸ“… 1981 πŸ› John Wiley and Sons 🌐 English βš– 483 KB

By JAMES A. RATE and JOHN K . LUEDEMAN of Clemson (I7.S.A.) (Eingegangen am 22. 11. 1979) REES matrix semigroups &I= (S, ,I, -1, P) over a semigroup correspond loosely to the n X n matrix rings over it ring R. It is well known that &(R,)x .=(&(R)),,. Moreover, when S is it finite BRANDT semigroup, S