Talk:Baer ring

It might be better to assume unity

I have not really seen much evidence that any of these definitions are used in rings without unity. I'm not an operator theorist though, so it could be less rare than I think. If it really is uncommon, then it would seem better to avoid all the "if it has unity... if it has unity..." business. Frankly speaking, I feel like rings without unity are the exception, not the other way around. In any case I would be interested in suggested sources for Baer and Rickart rings without unity, and hearing the opinion from the rings without unity camp. Thanks, Rschwieb (talk) 06:05, 20 March 2011 (UTC) UPDATE: I notice Berberian's contains the phrase "without unity" in some exercises, but still here, it looks like they are only concerned with *-rings, where I gather the definitions are still left-right symmetric. Rschwieb (talk) 20:11, 20 March 2011 (UTC)

The standard example for rings without unity are those built from functions that vanish at infinity. (viz functions over some non-compact manifold, and you want to limit yourself to the well-behaved ones or integrable ones, or whatever.) This seems "common enough" to me. I cannot give an explicit example that obeys all the axioms of a Baer ring, but that's only out of laziness. linas (talk) 19:08, 4 April 2026 (UTC)