Extensions of reversible rings.
A ring \(R\) is called reversible if \(ab = 0\) implies \(ba = 0\) for \(a,b\) \(\in R\). Some authors call this ring zero-commutative. The authors obtain some basic properties of basic extensions of these rings. Let \(T(R,R)\) and \(R[x]\) be the \(2\) by \(2\) upper triangular matrix ring and polynomial ring over \(R\), respectively. If \(R\) is reduced (i.e., there are no non-zero nilpotent elements in \(R\)), the authors prove that \(T(R,R)\) and \(R[x]/ (x^n)\) are reversible rings, where \((x^n)\) is the ideal of \(R[x]\) generated by \(x^n\).
scientific article; zbMATH DE number 2005928