Is there any essential difference between an (associative) algebra (over a field or a ring) and a (possibly non-commutative, non-unital) ring? Is there any essential difference between a field extension and a (commutative, associative, unital) division algebra over a field?
Would it be wrong to regard an algebra as a generalisation of a ring, rather than a sort of vector space / module with a bilinear multiplication?
Algebras vs rings Watch
- Thread Starter
- 12-12-2010 15:57
- 12-12-2010 16:55
Isn't an associative algebra a type of ring?