6533b7d9fe1ef96bd126c09e
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On many-sorted algebraic closure operators
Juan Soliveres TurJuan Climent Vidalsubject
Algebraic cycleDiscrete mathematicsGeneral MathematicsAlgebraic surfaceReal algebraic geometryAlgebraic extensionDimension of an algebraic varietyAlgebraic functionOperator theoryAlgebraic closureMathematicsdescription
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)
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-03-01 | Mathematische Nachrichten |