Rectangular loops


Aleksandar Krapež


Rectangular groups i.e. direct products of rectangular bands and groups play a significant role in the semilattice decomposition theory of semigroups. In our attempt to generalize this theory to groupoids, we start by investigating {\it rectangular loops} i.e. direct products of rectangular bands and loops. The standard method of R. A. Knoebel gives us an axiom system for rectangular loops consisting of 21 identities in an extended language. We give a simpler and more intuitive equivalent system of only 12 identities. Other important properties of rectangular loops are derived.