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Binary Operations - Introduction to Abstract Algebra - Exam

Exams, Algebra

Post: February 14th, 2013
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This is the Exam of Introduction to Abstract Algebra and its key important points are: Binary Operations, Mapping, Common Factor, Highest Common Factor, Pair of Integers, Euclidean Algorithm, Different Pairs, Divisibility, Principal Residues, Multiplication Tables
This is the Exam of Introduction to Abstract Algebra and its key important points are: Binary Operations, Mapping, Common Factor, Highest Common Factor, Pair of Integers, Euclidean Algorithm, Different Pairs, Divisibility, Principal Residues, Multiplication Tables
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Contents
PRIFYSGOL CYMRU/UNIVERSITY OF WALES ABERYSTWYTH INSTITUTE OF MATHEMATICS AND PHYSICS SEMESTER 1 EXAMINATIONS, JANUARY/FEBRUARY 2010 MA20310 - Introduction to Abstract Algebra Time allowed - 2 hours • Full marks will be given for complete answers to all questions in section A and to three questions in section B. In section B, credit will be given to the best three questions answered. • Calculators are not permitted. 18/12/2009 MA20310 - Introduction to Abstract Algebra 2 of 6 Section A 1. (a) Let A and B be sets. Give the definitions of a mapping F : A → B , and of a binary operation on A. [3 marks] (b) Let ⊕ and ⊗ be binary operations on Z × N as follows: (k, l) ⊕ (m, n) = (kn + lm, ln) (k, l) ⊗ (m, n) = (km, ln) i) Compute (7, 2) ⊕ (−3, 4) and (−7, 3) ⊗ (4, 2). ii) Show that, for all a, b, c ∈ Z × N, (a ⊕ b) ⊕ c = a ⊕ (b ⊕ c) . iii) Find u ∈ Z × N such that u ⊗ a = a, for all a ∈ Z × N. [2 marks] [4 marks] [2 marks] 2. (a) Define a co..

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