 A Bernstein algebra, based on the work of on the Hardy–Weinberg law in genetics, is a (possibly non-associative) baric algebra "B" over a field "K" with a weight homomorphism "w" from "B" to "K" satisfying formula_1.Every such algebra has idempotents "e" of the form formula_2 with formula_3.The Peirce decomposition of "B" corresponding to "e" is 
where formula_5 and formula_6.