My Math Forum

My Math Forum (http://mymathforum.com/math-forums.php)
-   Abstract Algebra (http://mymathforum.com/abstract-algebra/)
-   -   Question about def. of additive groups (http://mymathforum.com/abstract-algebra/15950-question-about-def-additive-groups.html)

studentx November 24th, 2010 04:21 AM

Question about def. of additive groups
 
Hi!

Just a little question about the def. of additive groups. It just mean a group whose binary operation we do not know, but
it is closed under addition righ? It does not mean that the groups binary operation necessarily is addition...

CRGreathouse November 24th, 2010 04:56 AM

Re: Question about def. of additive groups
 
It means a *group* whose operation we call "addition". So not only is it closed under the operation, but it is associative under the operation and there is an inverse for that operation.

The Chaz November 24th, 2010 05:49 AM

Re: Question about def. of additive groups
 
Also, the notation is a bit different.
Rather than writing
a ? (a^-1) = e
(where e is the identity element), you can write
a + (-a) = 0
since the additive inverse of an element is its opposite/negative.

Turgul November 24th, 2010 05:55 AM

Re: Question about def. of additive groups
 
It tends to be contextual as to whether a group is written additively or multiplicatively. By convention, groups are almost never written additively if they are not Abelian (commutative with respect to the operation). Strictly speaking however, the only difference is one of notation, as noted above.

studentx November 24th, 2010 06:57 AM

Re: Question about def. of additive groups
 
mhm, ok I see. Thanks for all the feedback.


All times are GMT -8. The time now is 11:32 PM.

Copyright © 2019 My Math Forum. All rights reserved.