Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 0705.4132

Noetherian ring with free additive groups

Gershon Sageev·Saharon Shelah
View original source ↗Read source document ↗Export metadata ↓

Abstract

There are Noetherian rings (in fact domains) with a free additive group, in every infinite cardinality. (This is an expanded version of [SgSh:217] which appears in the Abstracts of the American Mathematical Society 7 (1986): 369.)

Explore related subjects

math.LO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gershon Sageev, Saharon Shelah. 2007-05-29. Noetherian ring with free additive groups. https://arxiv.org/abs/0705.4132

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Model completeness for the differential field of transseries with exponentiation

We show that the expansion of the valued differential field of logarithmic-exponential transseries by its natural exponential function is model complete. We give an axiomatization of the theory of this expansion that is effective relative to the theory of the real exponential field, and show that any maximal Hardy field satisfies the same axioms. We use this to prove a transfer theorem between Hardy fields and transseries.

math.LO↗
arXiv2026

Extended Frege proofs, circuits and rewriting

Inspired by a statement about Extended Frege proof systems by Jain and Jin (FOCS 2022) we prove that: - there is a p-time binary relation $\approx$ between circuits that implies their logical equivalence, - if the equivalence $C \equiv D$ has an Extended Frege or a Circuit Frege proof with $k$ steps then there is a chain of circuits $E_i$ $$ C = E_0 \approx \dots \approx E_t = D $$ with $t \le O(k \log k)$, and the total size of the chain is bounded above by $(k+|C|+|D|)^{O(1)}$.

math.LO↗
arXiv2026

A Zero--One Law for Subrings of the Reals Closed under Binary Interleaving

Erdős Problem 1154 asks whether every number in $[0,1]$ occurs as the Hausdorff dimension of a subring or subfield of $\mathbb{R}$. We prove that a subring of $\mathbb{R}$ closed under binary interleaving has Hausdorff dimension either zero or one. Consequently, every Turing ideal and its associated subfield satisfy the same dichotomy.

math.LO↗