Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am currently reading Dummit and Foote's Abstract Algebra, and am having a little confusion over the following excerpt:

Suppose that $*$ is a binary operation on a set $G$ and $H$ is a subset of $G$. If the restriction of $*$ to $H$ is a binary operation on $H$, i.e., for all $a,b \in H$, $a * b \in H$, then $H$ is said to be closed under $*$. Observe that if $*$ is an associative (respectively, commutative) binary operation on $G$ and $*$ restricted to some subset $H$ of $G$ is a binary operation on $H$, then $*$ is automatically associative (respectively, commutative) on $H$ as well.

What does it precisely does it mean to restrict a binary operator to the subset $H$?

share|improve this question

1 Answer 1

Restricting $*$ to the subset $H$ means forgetting (or not caring) what $a*b$ is when $a\notin H$ or $b\notin H$.

In other words, the restricted operator is the function $*':H\times H\to G$ defined by $h_1*'h_2=h_1*h_2$ for all $h_1,h_2\in H$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.