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Construct a field with 5 elements. Draw the tables of addition and multiplication. Hint 1. Let the elements of such a field be {0, 1, a, b, c}. Hint 2. use the cancellation rules, you may use the axioms and claim/propositions about fields in the course notes. You do not need to write all the reasoning only drawing the tables for addition and multiplication is enough (but make sure to understand the reasoning).

Construct a field with 5 elements. Draw the tables of addition and multiplication. Hint 1. Let the elements of such a field be {0, 1, a, b, c}. Hint 2. use the cancellation rules, you may use the axioms and claim/propositions about fields in the course notes. You do not need to write all the reasoning only drawing the tables for addition and multiplication is enough (but make sure to understand the reasoning).

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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Construct a field with 5 elements. Draw the tables of addition and multiplication. Hint 1. Let the elements of such a field be {0, 1, a, b, c}. Hint 2. use the cancellation rules, you may use the axioms and claim/propositions about fields in the course notes. You do not need to write all the reasoning only drawing the tables for addition and multiplication is enough (but make sure to understand the reasoning).
Transcribed Image Text:Construct a field with 5 elements. Draw the tables of addition and multiplication. Hint 1. Let the elements of such a field be {0, 1, a, b, c}. Hint 2. use the cancellation rules, you may use the axioms and claim/propositions about fields in the course notes. You do not need to write all the reasoning only drawing the tables for addition and multiplication is enough (but make sure to understand the reasoning).
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