## Missouri Journal of Mathematical Sciences

- Missouri J. Math. Sci.
- Volume 27, Issue 1 (2015), 64-70.

### General Dorroh Extensions

I. Alhribat, P. Jara, and I. Márquez

#### Abstract

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.

#### Article information

**Source**

Missouri J. Math. Sci., Volume 27, Issue 1 (2015), 64-70.

**Dates**

First available in Project Euclid: 3 December 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.mjms/1449161368

**Digital Object Identifier**

doi:10.35834/mjms/1449161368

**Mathematical Reviews number (MathSciNet)**

MR3431116

**Zentralblatt MATH identifier**

1337.16023

**Subjects**

Primary: 16D25: Ideals

Secondary: 16S70: Extensions of rings by ideals

**Keywords**

ring algebra Dorroh extension Szendrei extension

#### Citation

Alhribat, I.; Jara, P.; Márquez, I. General Dorroh Extensions. Missouri J. Math. Sci. 27 (2015), no. 1, 64--70. doi:10.35834/mjms/1449161368. https://projecteuclid.org/euclid.mjms/1449161368