MODNET
Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1816

Preprint Number 1816

Previous Next Preprint server


1816. Jamshid Derakhshan, Angus Macintyre
Axioms for Commutative Unital Rings elementarily Equivalent to Restricted Products of Connected Rings
E-mail:

Submission date: 17 July 2020

Abstract:

We give axioms in the language of rings augmented by a 1-ary predicate symbol Fin(x) with intended interpretation in the Boolean algebra of idempotents as the ideal of finite elements, i.e. finite unions of atoms. We prove that any commutative unital ring satisfying these axioms is elementarily equivalent to a restricted product of connected rings. This is an extension of the results in [elem-prod] for products. While the results in [elem-prod] give a converse to the Feferman-Vaught theorem for products, our results prove the same for restricted products. We give a complete set of axioms in the language of rings for the ring of adeles of a number field, uniformly in the number field.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2007.09244: pdf, ps.


Last updated: July 28 2020 13:53 Please send your corrections to: