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- Title
RADICALS AND EMBEDDINGS OF MOUFANG LOOPS IN ALTERNATIVE LOOP ALGEBRAS.
- Authors
Sandu, Nicolae I.
- Abstract
The paper defines the notion of alternative loop algebra F[Q] for any nonassociative Moufang loop Q as being any non-zero homomorphic image of the loop algebra FQ of a loop Q over a field F. For the class M of all nonassociative alternative loop algebras F[Q] and for the class L of all nonassociative Moufang loops Q are defined the radicals R and S, respectively. Moreover, for classes M, L is proved an analogue of Wedderburn Theorem for finite dimensional associative algebras. It is also proved that any Moufang loop Q from the radical class R can be embedded into the loop of invertible elements U(F[Q]) of alternative loop algebra F[Q]. The remaining loops in the class of all nonassociative Moufang loops L cannot be embedded into loops of invertible elements of any unital alternative algebras.
- Subjects
EMBEDDINGS (Mathematics); NONASSOCIATIVE rings; MOUFANG loops; ASSOCIATIVE algebras; NONASSOCIATIVE algebras
- Publication
ROMAI Journal, 2012, Vol 8, Issue 1, p115
- ISSN
1841-5512
- Publication type
Article