In this paper we proved that in a baric, power associative, F-algebra of finite dimension, there is an idempotent element of weight 1. When this algebra is alternative, with this idempotent we make the Peirces decomposition. We define the nil radical as the maximal nil ideal. We proved that the bar-radical is the intersection of the nil radical with the square of bara. All the results are naturally true for baric associative algebras of finite dimension. 1. Baric algebras. Baric algebras play a central role in the theory of genetic algebras. They were introduced by I. M. H. Etherington, [4], aiming for an algebraic treatment of Genetic Populations. Several classes of baric algebras have been defined: train, Bernstein, special triangular, etc.Let F be a field and a an algebra over F, not necessarily associative, commutative or finite dimensional. If wX a À3 F is a nonzero homomorphism, then the ordered pair aY w will be called a baric algebra over F and w its weight funcion or shortly its weight. For x P aY wx is called the weight of x. If b 7 a, we will denote barb fx P b X wx 0g. We observe that barb b if, and only if, b 7 bara.When b is a subalgebra of a and b 7 j bara, then b is called baric subalgebra of aY w. In this case bY w H is a baric algebra, where w H wj b X b À3 F. If b is a baric subalgebra of aY w and barb is a two-sided ideal of bara (then by [6, Prop. 1.1] it is also a two-sided ideal of a), then b is called normal baric subalgebra of aY w.Let b be a baric subalgebra of aY w. Then barb is a two-sided ideal of b of codimension 1. For all b P b with wb j 0, we have b Fb È barb. If I 7 barb is a two-sided ideal of b, then I is called a baric ideal of b. If I is a baric ideal of a and I does not contain any proper ideals of a, then I is called a simple baric ideal of a.