Graded reversibility in integral group rings. (Q1043832)

A ring is said to be reversible if \(ab=0\) implies \(ba=0\) for ring elements \(a\) and \(b\). Reversible rings were studied by \textit{P. M. Cohn} [Bull. Lond. Math. Soc. 31, No. 6, 641-648 (1999; Zbl 1021.16019)], reversible group rings by \textit{M. Gutan} and \textit{A. Kisielewicz} [J. Algebra 279, No. 1, 280-291 (2004; Zbl 1068.16033)]. Inspired by the results of \textit{Yu. A. Bahturin} and \textit{M. M. Parmenter}, [Lect. Notes Pure Appl. Math. 248, 25-32 (2006; Zbl 1102.16026)], the authors introduce the notion of graded reversibility, when the reversibility property is required for homogeneous elements only. \(C_2\)-graded integral group rings are characterized when the grading is induced by a subgroup of index 2 of the support group. Moreover, the authors give some improvements of results of the third paper cited above.