cyclic rings that are isomorphic to kkn


A finite cyclic ring of order ( n with behavior k is isomorphicPlanetmathPlanetmathPlanetmath to kZkn.


Note that kkn is a cyclic ring and that k is a generatorPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath of its additive groupMathworldPlanetmath. As groups, kkn and n are isomorphic. Thus, kkn has order n. Since k2=k(k), then k has behavior k. ∎

Title cyclic rings that are isomorphic to kkn
Canonical name CyclicRingsThatAreIsomorphicToKmathbbZkn
Date of creation 2013-03-22 16:02:45
Last modified on 2013-03-22 16:02:45
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 10
Author Wkbj79 (1863)
Entry type Corollary
Classification msc 16U99
Classification msc 13M05
Classification msc 13A99
Related topic MathbbZ_n