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Abstract Algebra : Introduction

Study concepts, example questions & explanations for Abstract Algebra

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Example Questions

Example Question #1 : Introduction

Which of the following is an identity element of the binary operation (*) ?

Possible Answers:

b*b=e

e*b=b^2

e*b=b

e*b=e^2

e*b=eb

Correct answer:

e*b=b

Explanation:

Defining the binary operation (*) will help in understanding the identity element. Say is a set and the binary operator is defined as $A\times A\rightarrow A$ for all given pairs in .

Then there exists an identity element in such that given,

$\\a,b,c \ \epsilon\ A$

$\\a*e=a, e*a=a \\b*e=b, e*b=b \\c*e=c,e*c=c$

Therefore, looking at the possible answer selections the correct answer is,

e*b=b

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Example Question #2 : Introduction

Which of the following illustrates the inverse element?

Possible Answers:

a*e=a

a*b=a

b*e=b

a*b=e

a*b=b

Correct answer:

a*b=e

Explanation:

For every element in a set, there exists another element that when they are multiplied together results in the identity element.

In mathematical terms this is stated as follows.

For every $a\ \epsilon\ S\ \exists\ b\ \epsilon\ S$ such that a*b=e where $e\ \epsilon\ S$ and is an identity element.

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Abstract Algebra : Introduction

Study concepts, example questions & explanations for Abstract Algebra

All Abstract Algebra Resources

Example Questions

Example Question #1 : Introduction

Example Question #2 : Introduction

All Abstract Algebra Resources

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