In this paper, following the slid product construction for loops with inverses of Pasotti and Zizioli [J Geom 100(1-2):129-145, 2011], we present the general setting in order to build up a new loop (L, circle plus) starting from loops (K, +(+) over cap) equipped with a well ordering "<=", and (P, +) with the same neutral element. The results established in the aforementioned note are generalized as well. Moreover we investigate the nuclei of L, the normality of subloops isomorphic to (K, +) and and discuss some examples.
Slid product of loops: A generalization
Pasotti S.
;
2014-01-01
Abstract
In this paper, following the slid product construction for loops with inverses of Pasotti and Zizioli [J Geom 100(1-2):129-145, 2011], we present the general setting in order to build up a new loop (L, circle plus) starting from loops (K, +(+) over cap) equipped with a well ordering "<=", and (P, +) with the same neutral element. The results established in the aforementioned note are generalized as well. Moreover we investigate the nuclei of L, the normality of subloops isomorphic to (K, +) and and discuss some examples.File in questo prodotto:
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