> If I >> remember correctly, an abelian group is a group that has an invertible >table. > >What is an "invertible table" ? By the way, a group is abelian if the >group operation is commutative.
Right. So, if you set up a table with all the set members on the horizontal and vertical, it'll form an invertible diagonal because xy = yx. So, a group has to be closed, ASSOCIATE, have an identity, and have an inverse? Whereas an abelian group has to have all the above, plus be commutative, right? It's been 6 months, at least.
>those axioms in (a) are those for an abelian group. >In most linear algebra courses, the definition of an (abelian) group >should at least be mentioned because > >- the axioms from (a) can be remembered easier.
I agree. It's odd...we focused on abelian groups (and groups in general) in algebraic structures. We never mentioned abelian groups in linear, even though it's considered a continuing course from algebraic. However, I think I sort of subconciously realized that the first 4 characteristics of a vector space were similar to the types of thing we studied in algebraic. The last 4 seemed common-sense-ish.
>- the definition of a field also includes them for the field addition.