Exercise 8.1. (1) Show that Z√−2] := {a + b√√−2 | a, b € Z} is a subring of C. (2) Find a subring R of C so that Z[√−2] ≤ R ≤ C.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
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Exercise 8.1.
(1) Show that Z√−2] := {a + b√√−2 | a, b € Z} is a subring of C.
(2) Find a subring R of C so that Z[√−2] ≤ R ≤ C.
Transcribed Image Text:Exercise 8.1. (1) Show that Z√−2] := {a + b√√−2 | a, b € Z} is a subring of C. (2) Find a subring R of C so that Z[√−2] ≤ R ≤ C.
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