Prove that RoR = id and that ooR = Roo-. Conclude that o = U is a map which satisfies UoU = id. Maps which are their own inverse are called involutions. They represent very simple types of dynamical systems. Hence the shift may be decomposed into a composition of two such maps. UoR where

Prove that RoR = id and that ooR = Roo-. Conclude that o = U is a map which satisfies UoU = id. Maps which are their own inverse are called involutions. They represent very simple types of dynamical systems. Hence the shift may be decomposed into a composition of two such maps. UoR where

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 6E

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Question

14. Let R: E2 → E2 be defined by
R(...s-2s-1.803132 -..) = (...323130.3-13–2 . ).
Prove that RoR = id and that ooR = Roo-. Conclude that o = UoR where
U is a map which satisfies U oU = id. Maps which are their own inverse are
called involutions. They represent very simple types of dynamical systems.
Hence the shift may be decomposed into a composition of two such maps.
%3D
%3D
%3D

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