Mathematical Structures: History of Quasigroups

# History of Quasigroups

 Revision 8 . . July 27, 2004 6:45 pm by Jipsen Revision 7 . . July 10, 2004 10:51 am by Jipsen Revision 6 . . (edit) April 18, 2003 10:53 pm by Peter Jipsen

Difference (from prior major revision) (author diff)

Changed: 32c32
 A quasigroup is a structure $\mathbf{A}=\langle A,\cdot ,\backslash,/\rangle$ of type $\langle 2,2,2\rangle$ such that
 A quasigroup is a structure $\mathbf{A}=\langle A,\cdot ,\backslash,/\rangle$ of type $\langle 2,2,2\rangle$ such that

Changed: 35c35
 $(y/x)x = y$, $x(x\y) = y$
 $(y/x)x = y$, $x(x\backslash y) = y$

Changed: 38c38
 $(xy)/y = x$, $x\(xy) = y$
 $(xy)/y = x$, $x\backslash(xy) = y$

Changed: 47,48c47
 $h(xy)=h(x)h(y)$, $h(x\backslash y)=h(x)\backslash h(y)$, $h(x/y)=h(x)/h(y)$
 $h(xy)=h(x)h(y)$, $h(x\backslash y)=h(x)\backslash h(y)$, $h(x/y)=h(x)/h(y)$.