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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.1: Rectangular Coordinate Systems
Problem 21E
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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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