Marc LeBrun <mlb@fxpt.com> wrote:
Mike Stay <staym@clear.net.nz> wrote:
Does this definition fit your structure? http://www.wikipedia.org/wiki/Rig_(algebra)
Yes it does, so "rig" it is I guess, thank you!
(The next closest contender was "semiring", but that needn't have identities).
Semiring and rig may be the same structure, and may or may not require additive neutral elements - depending on the author. However, semiring is far more widely used. For example, in the AMS Math Reviews database there are 1126 reviews containing "semiring" but only 3 containing "rig". In fact there are more references to oil rigs than to rigs as algebraic structures! Of those 3 references one is a 1990 paper by Schanuel [1] (is this the first use in print?), the second [2] is a 1991 paper on algebraic semantics of programming languages, and the third [3] is a 1993 paper on combinatorics (species). -Bill Dubuque [1] Schanuel, Stephen H. Negative sets have Euler characteristic and dimension. Category theory (Como, 1990), 379-385, Lecture Notes in Math., 1488, Springer, Berlin, 1991. http://www.ams.org/mathscinet-getitem?mr=93m:18011 [2] Heckmann, Reinhold Observable modules and power domain constructions. Semantics of programming languages and model theory (Schloss, Dagstuhl, 1991), 159-187, Algebra Logic Appl., 5, Gordon and Breach, Montreux, 1993. http://www.ams.org/mathscinet-getitem?mr=95e:68129 [3] Rajan, Dayanand S. The adjoints to the derivative functor on species. J. Combin. Theory Ser. A 62 (1993), no. 1, 93-106. http://www.ams.org/mathscinet-getitem?mr=94d:05145