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Upper bound for the length of commutative algebras

โœ Scribed by Markova, Ol'ga V


Book ID
120157904
Publisher
Turpion Limited
Year
2009
Tongue
English
Weight
331 KB
Volume
200
Category
Article
ISSN
1064-5632

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Let F be a field, and let A be a finite-dimensional F-algebra. Write d s dim A, F and let e be the largest degree of the minimal polynomial for any a g A. Define ลฝ . ' the function f d, e s e 2dr e y 1 q 1r4 q er2 y 2. We prove that, if S is ลฝ . any finite generating set for A as an F-algebra, the

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In recent years, several eigenvalues, norms and determinants bounds have been investigated separately for the solutions of continuous and discrete Riccati equations. In this paper, an upper bound for solution of the unified Riccati equation is presentec~. In the limiting cases, the result reduces to