Search results for "Algebraic extension"
showing 6 items of 6 documents
On many-sorted algebraic closure operators
2004
A theorem of Birkhoff-Frink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the corresponding generated subalgebra operator. However, for many-sorted sets, i.e., indexed families of sets, such a theorem is not longer true without qualification. We characterize the corresponding many-sorted closure operators as precisely the uniform algebraic operators. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Asymptotically good codes from generalized algebraic-geometry codes
2005
We consider generalized algebraic-geometry codes, based on places of the same degree of a fixed algebraic function field over a finite field. In this note, using a method similar to the Justesen's one, we construct a family of such codes which is asymptotically good.
ON AUTOMORPHISMS OF GENERALIZED ALGEBRAIC-GEOMETRY CODES.
2007
Abstract We consider a class of generalized algebraic-geometry codes based on places of the same degree of a fixed algebraic function field over a finite field F / F q . We study automorphisms of such codes which are associated with automorphisms of F / F q .
Algebraic time-reversal operation
1999
International audience; We analyze the implementation of the time-reversal (TR) transformation in the algebraic approach to tetrahedral local molecules through the chain of groups U(5) U(4) K(4) = A(4) ^ S(4) S(4) Td. We determine the general form of the TR operation using a purely algebraic realization, based exclusively on the requirement that the irreducible representations must not be changed under the time inversion symmetry. As a result we can determine the TR behavior of purely algebraic operators.
General Theory: Algebraic Point of View
2009
It is convenient to divide our study of pip-spaces into two stages. In the first one, we consider only the algebraic aspects. That is, we explore the structure generated by a linear compatibility relation on a vector space V , as introduced in Section I.2, without any other ingredient. This will lead us to another equivalent formulation, in terms of particular coverings of V by families of subspaces. This first approach, purely algebraic, is the subject matter of the present chapter. Then, in a second stage, we introduce topologies on the so-called assaying subspaces \(\{V_r \}\). Indeed, as already mentioned in Section I.2, assuming the partial inner product to be nondegenerate implies tha…
Commutative Partial O*-Algebras
2002
This chapter is devoted to the integrability of commutative partial O*-algebras. Three notions of weak commutativity, commutativity and strong commutativity of an O*-vector space are defined and investigated. In Section 3.1, we analyze the relation between the integrability of weakly commutative O*-vector space M and the commutativity of the von Neumann algebra (M w ′ )′. In Section 3.2, we study the integrable extensions of partial O*-algebras. In Section 3.3, we describe another explicit example, namely, the partial O*-algebra M[S, T] generated by two weakly commuting symmetric operators S and T defined on a common dense domain in a Hilbert space. In particular, we investigate in detail t…