Remarks on a Paper of Wagner Original Research Article

Ifgandhare integers greater than 1, a ringWsubset of or equal toimage is called a Wagner ring of type (g; h) if allxset membership, variantW\{0} are normal to basegbut non-normal to baseh. The existence of such rings was shown in 1989 by Wagner for the case whengis a proper odd prime divisor ofhwith (g, (h/g))=1. This result is generalized to the case of arbitrary pairs of integersg, hwithgmidhsuch that there exists a primep1withp1does not divideg, p1mid(h/g).