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On constructivity of involutive divisions

โœ Scribed by A. S. Semenov

Book ID
110190819
Publisher
SP MAIK Nauka/Interperiodica
Year
2006
Tongue
English
Weight
169 KB
Volume
32
Category
Article
ISSN
0361-7688

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Let D be a division algebra of degree 3 over its center K and let J be an involution of the second kind on D. Let F be the subfield of K of elements invariant under J, char F / 3. We present a simple proof of a theorem of A. Albert on the existence of a maximal subfield of D which is Galois over F w

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Generalising the divisibility relation of terms we introduce the lattice of so-called involutive divisions and define the admissibility of such an involutive division for a given set of terms. Based on this theory we present a new approach for building a general theory of involutive bases of polynom