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Let R = ({0, 1,,8), 0, 0) be a ring where and are defined as follows: a b = (a + b) mod 9 a Ob= (ab) mod 9 a) Find the zero element of R. b) Find the unit element of R, if it exists. c) If the unit element of R exists, find all zero divisors of R. d) Is R a field?

Let R = ({0, 1,,8), 0, 0) be a ring where and are defined as follows: a b = (a + b) mod 9 a Ob= (ab) mod 9 a) Find the zero element of R. b) Find the unit element of R, if it exists. c) If the unit element of R exists, find all zero divisors of R. d) Is R a field?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let R = ({0, 1,,8), 0, 0) be a ring where a and are defined as follows: b = (a + b) mod 9 ab (ab) mod 9 a) Find the zero element of R. b) Find the unit element of R, if it exists. c) If the unit element of R exists, find all zero divisors of R. d) Is R a field?
Transcribed Image Text:Let R = ({0, 1,,8), 0, 0) be a ring where a and are defined as follows: b = (a + b) mod 9 ab (ab) mod 9 a) Find the zero element of R. b) Find the unit element of R, if it exists. c) If the unit element of R exists, find all zero divisors of R. d) Is R a field?
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