Podcast
Questions and Answers
What is the role of an identity element in a group?
What is the role of an identity element in a group?
It has no effect on the effect or purpose of the operation.
Define an invertible element in a group.
Define an invertible element in a group.
An element whose operation with its inverse element results in the identity element.
What is the main difference between a semigroup and a group?
What is the main difference between a semigroup and a group?
A group has an identity element and every element is invertible, while a semigroup does not necessarily have these properties.
Why are not all elements in a semigroup invertible?
Why are not all elements in a semigroup invertible?
What properties must a set R satisfy to be considered a ring?
What properties must a set R satisfy to be considered a ring?
Provide an example of a classic ring.
Provide an example of a classic ring.
What is the defining property of a group?
What is the defining property of a group?
In a semigroup, what element may or may not exist?
In a semigroup, what element may or may not exist?
Which set does not have invertible elements?
Which set does not have invertible elements?
What is the role of a neutral element in a semigroup?
What is the role of a neutral element in a semigroup?
What is the defining property of a ring?
What is the defining property of a ring?
Which pair of operations defines a ring?
Which pair of operations defines a ring?
What is the unique property of the identity element in a group?
What is the unique property of the identity element in a group?
Why are not all elements in every semigroup invertible?
Why are not all elements in every semigroup invertible?
