The intersection property of quasi-ideals in rings and semigroup rings
A ring means an associative ring. Let \(A\) be a ring. A subgroup \(Q\) of the group \((A,+)\) is called a quasi-ideal of \(A\) iff \(AQ\cap QA\subseteq Q\). A trivial example of a quasi-ideal in a ring \(A\) is \(L\cap R\), where \(L\) is a left and \(R\) is a right ideal of \(A\). It is known that this construction does not give all quasi-ideals of a ring in general. The authors present a partial solution for problems raised by \textit{H. J. Weinert} [Acta Math. Hung. 43, 85-99 (1984; Zbl 0533.16018)] concerning rings (in particular, contracted semigroup rings) in which every quasi-ideal in fact is the intersection of a left and a right ideal.
scientific article; zbMATH DE number 894962
scientific article