MULTIPLICATIVE SUBSETS OF ATOMS

Year 2015, Volume: 18 Issue: 18, 107 - 116, 01.12.2015

Ashley Rand

https://doi.org/10.24330/ieja.266207

Cited By: 1

Abstract

A reduced, cancellative, torsion-free, commutative monoid M can
be embedded in an integral domain R, where the atoms (irreducible elements)
of M correspond to a subset of the atoms of R. This fact was used by J.
Coykendall and B. Mammenga to show that for any reduced, cancellative,
torsion-free, commutative, atomic monoid M, there exists an integral domain
R with atomic factorization structure isomorphic to M. More generally, we
show that any “nice” subset of atoms of R can be realized as the set of atoms
of an integral domain T that contains R. We will also give several applications
of this result.

Keywords

Cancellative commutative monoid, reduced monoid, atomic monoid, integral domain