General Dorroh Extensions

Abstract

In a recent paper G. A. Cannon and K. M. Neuerburg point out that if A = Z and B is an arbitrary ring with unity, then Z*B, the Dorroh extension of B, is isomorphic to the direct product Z×B. Thus, the ideal structure of Z*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 heir behavior with respect to algebra maps.