Missouri Journal of Mathematical Sciences

Ideals in Dorroh Extensions of Rings

G. Alan Cannon and Kent M. Neuerburg

Full-text: Open access


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 $R$.

Article information

Missouri J. Math. Sci., Volume 20, Issue 3 (2008), 165-168.

First available in Project Euclid: 14 September 2011

Permanent link to this document

Digital Object Identifier

Zentralblatt MATH identifier

Primary: 16D25: Ideals
Secondary: 16S99: None of the above, but in this section


Cannon, G. Alan; Neuerburg, Kent M. Ideals in Dorroh Extensions of Rings. Missouri J. Math. Sci. 20 (2008), no. 3, 165--168. doi:10.35834/mjms/1316032775. https://projecteuclid.org/euclid.mjms/1316032775

Export citation