The universal associative enveloping algebra of a Lie-Jordan algebra with a unit

We describe the universal associative enveloping algebra of a Lie-Jordan algebra with a unit over a field of characteristic 0. We show that if L is a Lie-Jordan algebra with a unit e over a field F of characteristic 0, then the (unital) universal associative envelope of L is isomorphic to F . 1 circle plus L circle plus eL, where eL = {ex vertical bar x is an element of L}. The center of the universal associative envelope is also described. We conclude the paper with some open problems for further research.