Talk:Simple algebra (universal algebra)

"The second condition in the definition precludes the following situation: consider the algebra

   \{ \begin{bmatrix} 0 & \alpha \\ 0 & 0 \\ \end{bmatrix}\, | \, \alpha \in \mathbb{C} \}

with the usual matrix operations"

in my opinion, this is NOT algebra, because there is not "1". And the algebra HAS (in respect to this wikipedia page: http://en.wikipedia.org/wiki/Algebra_%28ring_theory%29) to be a ring with unit! I hope that my terrible english is comprehensible at least--80.180.27.186 (talk) 08:32, 11 September 2009 (UTC)[reply]

Please note that the terms "algebra" and "ring" are not always consistently defined in the literature. For my applications they are both usually commutative with a unit element, which is why one drops saying this all the time. In representation theory it makes sense that they are usually only assumed to be associative. However, as Wikipedia is a comprehensive resource, it makes therefore more sense to not impose these assumptions, but rather mention them every time that you really want to assume them, although it might be tedious sometimes. 178.6.215.188 (talk) 13:23, 3 January 2020 (UTC)[reply]