A number of papers have appeared with the purpose of generalizing Albert’s long-standing result [l, 21 that a simple right alternative algebra of finite dimension over a field of characteristic f2 that has a unit element e and an idempotent c # e is necessarily alternative. Until now results depended on rather strong additional assumptions such as other identities [S, 14, 17, 36, 371 or internal conditions on the algebra [9, 10, 12, 15, 27, 28, 301. Essential progress has been achieved by Micheev who showed that the identity (x, x, Y)~ = 0 holds in 2-torsion free right alternative algebras [27]. This paper starts collecting information on two natural concepts in a right alternative algebra R, the submodule M generated by all alternators (x, x, y), and a new nucleus N, . The later sections deal mainly with results on simple right alternative algebras. A simple 2-torsion free right alternative algebra is either alternative, hence associative or a Cayley algebra over its center, or the following statements hold: