The unit sum number of Baer rings. (English) Zbl 1373.16063
Summary: In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of \(R\) is isomorphic to \(Z_2\) and we characterize regular Baer rings with unit sum numbers \(\omega\) and \(\infty\). Then as an application, we discuss the unit sum number of some classes of group rings.
MSC:
16U60 | Units, groups of units (associative rings and algebras) |
16S34 | Group rings |
16D10 | General module theory in associative algebras |