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
โฆ LIBER โฆ
Upper bound for the length of commutative algebras
โ 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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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