Abstract Algebra : Introduction

Study concepts, example questions & explanations for Abstract Algebra

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Example Questions

Example Question #1 : Groups

Which of the following is an identity element of the binary operation ?

Possible Answers:

Correct answer:


Defining the binary operation  will help in understanding the identity element. Say  is a set and the binary operator is defined as  for all given pairs in .

Then there exists an identity element  in  such that given,

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

Example Question #2 : Abstract Algebra

Which of the following illustrates the inverse element?

Possible Answers:

Correct answer:


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  such that  where  and  is an identity element.

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