Abstract
The aim of this paper is the construction of free nuclear Jordan-Bernstein algebras, that is, the largest nuclear Jordan-Bernstein algebra generated by a set of generators. In this way, it is proved that every nuclear Jordan-Bernstein algebra is a quotient of an adequate free nuclear Jordan-Bernstein algebra. The same construction may be made without the nuclear assumption and free Jordan-Bernstein algebras may be constructed and related to free nuclear Jordan-Bernstein algebras. The nilpotency index of these algebras is studied, which lets us get a good bound for the nilpotency index in every Jordan-Bernstein algebra and in every nuclear Bernstein algebra. Finally, we can apply the obtained results to get some information about inner derivations of Jordan-Bernstein algebras.
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