Polynomial Identities for Bernstein Algebras of Simple Mendelian Inheritance

Abstract

The Bernstein algebra D n G α of simple Mendelian inheritance is the n-fold duplicate of the gametic algebra G α with basis A 1,…, A α and structure constants . We simplify and generalize results of Bernad et al. and Peresi by showing that every identity for G α follows from Costa's shape identity C, and that every identity for the zygotic algebra DG α follows from the recombination identity R. We use computer algebra to determine the identities of degree ≤7 for the copular algebra D 2 G α.