Geodesic
Rectangular loops
Publications de l'Institut Mathématique, _N_S_68 (2000) no. 82, p. 59 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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.
Classification : 20N02
Keywords: groupoid, rectangular loop, axiomatization, axiom independence, word problem 
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     author = {Aleksandar Krape\v{z}},
     title = {Rectangular loops},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {59 },
     year = {2000},
     volume = {_N_S_68},
     number = {82},
     zbl = {0971.20047},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2000_N_S_68_82_a5/}
}
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Aleksandar Krapež. Rectangular loops. Publications de l'Institut Mathématique, _N_S_68 (2000) no. 82, p. 59 . http://geodesic.mathdoc.fr/item/PIM_2000_N_S_68_82_a5/