Talk:Operator algebra

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It would be nice to have at least one example of an Operator Algebra. Most of the other pages on mathematical objects list a few examples. CarlFeynman (talk) 23:06, 4 May 2011 (UTC)[reply]

This page says "Operator algebras are in general non-commutative rings" Whereas, the page about rings say rings have to have the property that their operators are commutative. What gives? —Preceding unsigned comment added by 76.23.104.212 (talk) 20:44, 13 May 2011 (UTC)[reply]

In general, a ring's product is not necessarily commutative. Some authors, the ones who will only be talking about commutative rings, include commutativity in the definition for convenience. It's just a matter of convention. The phrase "non-commutative ring" refers to a ring whose product is not assumed to be commutative. However, I think the Wikipedia page on rings should not include commutativity since the "standard" definition does not. 70.30.23.131 (talk) 16:53, 5 June 2014 (UTC)[reply]