colonel@ellie.UUCP (Col. G. L. Sicherman) (03/12/86)
> You might be interested in loops, where the multiplication has > different left and right inverses. Unfortunately, elementary > accounts are rare. There is a volume in the Springer Ergebnisse > series on loops, written by Bruck. They're useful for representing > Latin Squares. There's a more recent reference which currently > escapes me. The last book I read on Latin Squares called them "quasigroups" or something like that. "Loops" sounds much better--if they're indeed the same. "An antiset is a mathematical object that fails to contain each of its members." --E. P. B. Umbugio -- Col. G. L. Sicherman UU: ...{rocksvax|decvax}!sunybcs!colonel CS: colonel@buffalo-cs BI: csdsicher@sunyabva
kwh@bentley.UUCP (KW Heuer) (03/16/86)
In article <886@ellie.UUCP> ellie!colonel (Col. G. L. Sicherman) writes: >The last book I read on Latin Squares called them "quasigroups" or >something like that. "Loops" sounds much better--if they're indeed >the same. If I remember correctly, a loop is a quasigroup with an identity element. The quasigroup axioms include cancellation (if xz=yz or zx=zy then x=y) but not associativity; an associative quasigroup (or loop) is a group. Another way to say this is that an object which is both a quasigroup and a semigroup is a group. What's the origin of the name "Loop"? Is it a contraction of "Latin- square group", or what? (I see nothing that suggests roundness in either loops or rings.)
ladkin@kestrel.ARPA (Peter Ladkin) (03/18/86)
In article <886@ellie.UUCP>, colonel@ellie.UUCP (Col. G. L. Sicherman) writes: > > The last book I read on Latin Squares called them "quasigroups" or > something like that. "Loops" sounds much better--if they're indeed > the same. Whoops! I guess I don't have my definitions right. They're very close, but not the same. I think one has an identity and one not. Peter Ladkin