洪萬生2014-10-272014-10-271981-06-??http://rportal.lib.ntnu.edu.tw/handle/20.500.12235/16997Given two arbitary domains G, G' in Rn (n ≧ 3), L.G. Lewis proved that G and G' are quasi-conformally equivalent if and only if their Royden n-algebras are isomorplic. In this article, the analagous results are established for quasi-regular mappings. The author proves that (1) if F:G→G' (G'=F (G) ) is quasiregular, then the Royden n-algebra Mn (G') C 1 (G') can be imbedded into the Royden n-algebra Mn (G) as a subalgebra; and (2) if Royden p-algebras (p≧l) MP (G') and MP (G) are isomorphic, then F is a Qp-mapping. The special case p=n for (2) gives the coverse result of (1).Royden代數正則映像