Direct Sum vs Cartesian Product

Excellent explanation found on Math Stackexchange.

Basically for finite index sets (finite number of factors), the two constructions are the same.

Only when there is an infinite number of factors, the direct sum \bigoplus_{i\in I}G_i is the subgroup of the Cartesian product consisting of all tuples \{g_i\} where there are only finitely many g_i that are nonzero.

About mathtuition88
This entry was posted in Algebra and tagged . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.