From Involution Sets, Graphs and Loops to Loop-Nearrings

Helmut Karzel (), Silvia Pianta () and Elena Zizioli ()
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Helmut Karzel: Zentrum Mathematik, T. U. München
Silvia Pianta: Università Cattolica, Dipartimento di Matematica e Fisica
Elena Zizioli: Università degli Studi di Brescia, Dipartimento di Matematica, Facoltà di Ingegneria

A chapter in Nearrings and Nearfields, 2005, pp 235-252 from Springer

Abstract: Abstract This is a general frame for a theory which connects the areas of loops, involution sets and graphs with parallelism. Our main results are stated in §5, §6 and §7. In §5 we derive a partial binary operation from an involution set and we discuss if such operation is a Bol operation or a K-operation, in §6, we relate involution sets with loops. In §7 we look for the possibility to construct loop-nearrings by considering the automorphism groups of loops.

Keywords: graphs; loops; involution sets; loop-nearrings (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/1-4020-3391-5_12

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