On decomposition of commutative Moufang groupoids
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چکیده
X iv :0 80 3. 04 72 v1 [ m at h. R A ] 4 M ar 2 00 8 On decomposition of commutative Moufang groupoids B.V.Novikov It is well-known that the multiplicative groupoid of an alternative/Jordan algebra satisfies Moufang identities [1, 4]. Therefore it seems interesting to study the structure of such groupoids. In this note we apply to Moufang groupoids an approach which is widespread in Semigroup Theory — decomposition into a semilattice of subsemigroups [3]. We shall call a groupoid with the identity (xy)(zx) = (x(yz))x (1) by a Moufang groupoid. Everywhere in this article M denotes a commutative Moufang groupoid.
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