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Ultima descărcare din IBN: 2018-08-08 04:17 |
SM ISO690:2012 SANDU, Nicolae. Free Moufang loops and alternative algebras. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2009, nr. 3(61), pp. 96-108. ISSN 1024-7696. |
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
Numărul 3(61) / 2009 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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Pag. 96-108 | ||||||
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Rezumat | ||||||
It is proved that any free Moufang loop can be embedded in to a loop of invertible elements of some alternative algebra. Using this embedding it is quite simple to prove the well-known result: if three elements of Moufang loop are bound by the associative law, then they generate an associative subloop. It is also proved that the intersection of the terms of the lower central series of a free Moufang loop is the identity and that a finitely generated free Moufang loop is Hopfian. |
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Cuvinte-cheie Moufang loop, lower central series, Hopfian loop, alternative algebra. |
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