von Neumann regular skew group rings.

摘要

Given a group G acting on a ring R, one can form the skew group ring R * G. We give conditions for a von Neumann regular skew group ring to be simple. We use this information to construct a class of examples of simple von Neumann regular skew group rings and show that two examples in the literature are isomorphic to skew group rings in this class. We then examine corners of skew group rings and show that although a corner of a skew group is not necessarily a skew group ring, in certain situations they contain corners which are skew group rings. Finally, we combine this with information about the stable range of a ring to get a result about the unit-regularity of skew group rings.