Definition talk:Ring (Abstract Algebra)

It's a trivial point, but my impression was that usually $R^*=$ the group of units of a ring, which usually gets defined by $R-0$ in texts when working only with fields. Could just be me though Linus44 08:38, 12 February 2011 (CST)

Recommend that when we need to use the concept of either the set of units or the ring less unity, if we use $R^*$ we make sure we define it first thing on the page. "Let $R$ be a ring and $R^*$ the set of units of that ring" or whatever (neater of course and linking to the appropriate definitions ;-) and then we'll know where we stand. --prime mover 14:26, 12 February 2011 (CST)

... I've put a note in on this page to indicate that there are different interpretations. --prime mover 14:30, 12 February 2011 (CST)

Isn't the additive group $(R,∗)$ supposed to be Abelian? --Alec (talk) 14:09, 30 May 2011 (CDT)

Sure thing. But as this can be deduced from the other axioms, I didn't include it as an axiom but added it as a theorem. This has now been referred to on the page so as to allay confusion. --prime mover 14:27, 30 May 2011 (CDT)