Journal of Commutative Algebra

Normsets of almost Dedekind domains and atomicity

Richard Erwin Hasenauer

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Abstract

In this paper, we will introduce a new norm map on almost Dedekind domains. We compare and contrast our new norm map to the traditional Dedekind-Hasse norm. We prove that factoring in an almost Dedekind domain is in one-to-one correspondence to factoring in the new normset, improving upon this results in \cite {Coykendall}. In \cite {Grams}, an atomic almost Dedekind domain was constructed with a trivial Jacobson radical. We pursue atomicity in almost Dedekind domains with nonzero Jacobson radicals, showing the usefulness of the new norm we introduced. We state theorems with regard to specific classes of almost Dedekind domains. We provide a necessary condition for an almost Dedekind domain with nonzero Jacobson radical to be atomic.

Article information

Source
J. Commut. Algebra, Volume 8, Number 1 (2016), 61-75.

Dates
First available in Project Euclid: 28 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.jca/1459169545

Digital Object Identifier
doi:10.1216/JCA-2016-8-1-61

Mathematical Reviews number (MathSciNet)
MR3482346

Zentralblatt MATH identifier
1343.13010

Subjects
Primary: 13A50: Actions of groups on commutative rings; invariant theory [See also 14L24]
Secondary: 13F15: Rings defined by factorization properties (e.g., atomic, factorial, half- factorial) [See also 13A05, 14M05]

Keywords
Factorization almost Dedekind

Citation

Hasenauer, Richard Erwin. Normsets of almost Dedekind domains and atomicity. J. Commut. Algebra 8 (2016), no. 1, 61--75. doi:10.1216/JCA-2016-8-1-61. https://projecteuclid.org/euclid.jca/1459169545


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References

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