So magma is a name used for that. I was introduced to it as "groupoid" in the 1968 book _Introduction to Algebraic Structures_ by Azriel Rosenfeld. The EIS has called them groupoids since before I knew about it. (The wikipedia article mentions the name also.) Then there's that annoying fact that "groupoid" also refers to group-like categories, so maybe a new name is needed to avoid confusion. Then, too often, the things that should avoid confusion only create more. Regarding Rich's counts, since commutivity + idempotent ==> Rich's condition, the all idempotent case is given by A030257. Christian ------ Original Message ------ Received: Tue, 14 Feb 2006 04:54:40 AM PST From: dasimov@earthlink.net To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] AB = B.AA seems to imply commutativity?
Rich writes:
<< I've been exploring the binary operator *, which satisifies the rule A*B = B*(A*A). I like to write it in dot notation as AB = B.AA . [snip]
I just learned the word "magma" for a set S together with a binary operation *. Call this magma (S,*).
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