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arXiv · 1512.05024

The number of atoms in an atomic domain

Pete L. Clark·Saurabh Gosavi·Paul Pollack
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Abstract

We study the number of atoms and maximal ideals in an atomic domain with finitely many atoms and no prime elements. We show in particular that for all $m,n \in \mathbb{Z}^+$ with $n \geq 3$ and $4 \leq m \leq \frac{n}{3}$ there is an atomic domain with precisely $n$ atoms, precisely $m$ maximal ideals and no prime elements. The proofs use both commutative algebra and additive number theory.

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Pete L. Clark, Saurabh Gosavi, Paul Pollack. 2015-12-16. The number of atoms in an atomic domain. https://arxiv.org/abs/1512.05024

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