Cyclic coverings of virtual link diagrams

A virtual link diagram is called mod m almost. classical if it admits an Alexander numbering valued in integers modulo m, and a virtual link is called mod m almost classical if it has a mod m almost classical diagram as a representative. In this paper, we introduce a method of constructing a mod m almost. classical virtual link diagram from a given virtual link diagram, which we call an m-fold cyclic covering diagram. The main result is that m-fold cyclic covering diagrams obtained from two equivalent virtual link diagrams are equivalent. Thus, we have a well-defined map from the set of virtual links to the set of mod m almost classical virtual links. Some applications are also given.