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October 2008 Ideals in Dorroh Extensions of Rings
G. Alan Cannon, Kent M. Neuerburg
Missouri J. Math. Sci. 20(3): 165-168 (October 2008). DOI: 10.35834/mjms/1316032775

Abstract

The Dorroh extension is typically applied to embed a ring without unity into a ring containing unity. However, de Alwis investigated the ring resulting from applying this extension to the ring of integers. We show that the Dorroh extension of any ring with unity is isomorphic to a direct product of rings. Using this isomorphism we are able to verify the results of de Alwis and extend them to the Dorroh extension of any ring with unity. Also, given any ring $R$, we give conditions under which an ideal of the Dorroh extension $\mathbb{Z} * R$ can be expressed as a product (in the extension) of an ideal in $\mathbb{Z}$ and an ideal in $R$.

Citation

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G. Alan Cannon. Kent M. Neuerburg. "Ideals in Dorroh Extensions of Rings." Missouri J. Math. Sci. 20 (3) 165 - 168, October 2008. https://doi.org/10.35834/mjms/1316032775

Information

Published: October 2008
First available in Project Euclid: 14 September 2011

zbMATH: 1174.16001
Digital Object Identifier: 10.35834/mjms/1316032775

Subjects:
Primary: 16D25
Secondary: 16S99

Rights: Copyright © 2008 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.20 • No. 3 • October 2008
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