The number of atoms in an atomic domain

Paul Pollack; Pete L. Clark; Saurabh Gosavi

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The number of atoms in an atomic domain

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arxiv 1512.05024 v1 pith:ZW6ZKKZ7 submitted 2015-12-16 math.AC math.NT

The number of atoms in an atomic domain

Pete L. Clark , Saurabh Gosavi , Paul Pollack This is my paper

classification math.AC math.NT

keywords atomsatomicdomainnumberelementsidealsmaximalprecisely

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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.

The number of atoms in an atomic domain

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