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November 2015 General Dorroh Extensions
I. Alhribat, P. Jara, I. Márquez
Missouri J. Math. Sci. 27(1): 64-70 (November 2015). DOI: 10.35834/mjms/1449161368


In a recent paper G. A. Cannon and K. M. Neuerburg point out that if $A=\mathbb{Z}$ and $B$ is an arbitrary ring with unity, then $\mathbb{Z}\star{B}$, the Dorroh extension of $B$, is isomorphic to the direct product $\mathbb{Z}\times{B}$. Thus, the ideal structure of $\mathbb{Z}\star{B}$ can be completely described. The aim of this note is to point out that this result may be extended to any pair $(A,B)$ in which $B$ is an $A$-algebra with unity, and to study the construction of extensions of algebras without zero divisors and their behavior with respect to algebra maps.


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I. Alhribat. P. Jara. I. Márquez. "General Dorroh Extensions." Missouri J. Math. Sci. 27 (1) 64 - 70, November 2015.


Published: November 2015
First available in Project Euclid: 3 December 2015

zbMATH: 1337.16023
MathSciNet: MR3431116
Digital Object Identifier: 10.35834/mjms/1449161368

Primary: 16D25
Secondary: 16S70

Rights: Copyright © 2015 Central Missouri State University, Department of Mathematics and Computer Science


Vol.27 • No. 1 • November 2015
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