(a) Show that Z is a principal ideal ring. See Theorem 3.1 (b) Every homomorphic image of...
Question:
(a) Show that Z is a principal ideal ring. See Theorem 3.1
(b) Every homomorphic image of a principal ideal ring is also a principal ideal ring.
(c) Zm is a principal ideal ring for every m > 0.
Data from Theorem 3.1
Transcribed Image Text:
Theorem 3.1. Every subgroup H of the additive group Z is cyclic. Either H (0) or (m), where m is the least positive integer in H. IfH (0), then H is infinite. =
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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