Rings over which polynomial rings are semi-commutative.
A semi-commutative ring is a ring for which \(ab=0\) implies \(aRb=0\) for \(a,b\in R\). For such a ring \(R\), it is known that the polynomial ring \(R[x]\) need not be semi-commutative. The authors define and study strongly semi-commutative rings (SSC rings). By definition, this is a ring for which the associated polynomial ring will be semi-commutative. It is shown that the class of reversible rings (\(ab=0\) implies \(ba=0\)) is not comparable with that of the SSC rings. Construction techniques for SSC rings are given and a number of basic properties of these rings is established.
scientific article; zbMATH DE number 5656869