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*Prime Non-Commutative JB-Algebras**

Authors:	El Amin Kaidi; Campoy Antonio Morales; Palacios Angel Rodriguez

Institution:	Departamento de Algebra y Análisis Matemático, Universidad de Almería Facultad de Ciencias Experimentales, 04120-Almería, Spain Departamento de Análisis Matemático, Universidad de Granada Facultad de Ciencias, 18071-Granada, Spain

Abstract:	We prove that if A is a prime non-commutative JB-algebra whichis neither quadratic nor commutative, then there exist a primeC-algebra B and a real number ${lambda}$ with $1/2$ < ${lambda}$ $≤$ 1 such that A =B as involutive Banach spaces, and the product of A is relatedto that of B (denoted by ${circ}$ , say) by means of the equality xy= ${lambda}$ x ${circ}$ y+(1 – ${lambda}$ )y ${circ}$ x. 2000 Mathematics Subject Classification46K70, 46L70.

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