Computability in Europe 2006
Logical Approaches to Computational Barriers

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Regular Talk:
Do Noetherian modules have Noetherian basis functions?

Speaker: Júlia Zappe
Author(s): Peter Schuster and Júlia Zappe


It is known that if a module over a commutative ring
has a Noetherian basis function, then it is Noetherian.
We prove that in the presence of countable choice
also the reverse implication is constructively valid for
countable and strongly discrete modules. In particular,
we can deduce the Hilbert basis theorem for this class
of Noetherian modules from Tennenbaum's version for
modules with a Noetherian basis function.

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