MULTIPLICATIVE SUBSETS OF ATOMS

Ashley Rand

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

Article Details

MULTIPLICATIVE SUBSETS OF ATOMS

Authors:

Ashley Rand

Publisher:

Abdullah HARMANCI

Journal:

International Electronic Journal of Algebra 2015 Vol.18 Issue 18, pp.107-116

Document Type:

Article

Publication Date:

11/2015

Document Language:

Turkish

Document ID (Org No.):

2000718142

Frequency:

Monthly

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

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

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.

Article Details

MULTIPLICATIVE SUBSETS OF ATOMS

Authors: Ashley Rand

Publisher: Abdullah HARMANCI

Journal: International Electronic Journal of Algebra 2015 Vol.18 Issue 18, pp.107-116

Document Type: Article

Publication Date: 11/2015

Document Language: Turkish

Document ID (Org No.): 2000718142

Frequency: Monthly

eISSN: 1306-6048

pISSN: 1306-6048

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

Issues

Authors:

Ashley Rand

Publisher:

Abdullah HARMANCI

Journal:

International Electronic Journal of Algebra 2015 Vol.18 Issue 18, pp.107-116

Document Type:

Article

Publication Date:

11/2015

Document Language:

Turkish

Document ID (Org No.):

2000718142

Frequency:

Monthly

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

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