General Dorroh Extensions
2015
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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