An interesting application of algebra to genetics

From the beginnings algebraic methods were used for investigating genetic principles and structures. In particular, this is the case with so-called factor-union phenotype systems introduced by Cotterman ([1]). In these systems a set of properties can be assigned to each gene in such a way that phenotypes are determined by unions of these sets. These properties which can be considered to correspond to imaginary or actual physical factors may help in explaining and understanding the evolution and structure of phenotype systems. In the literature there exist several algorithms for deciding if a given phenotype system possesses a so-called factor-union representation and for constructing such a representation (cf. e.g. [7], [3] and [4]). (In [5] some results of [3] are generalized.) We mainly follow the method published in [4]. However, the presentation given here explains in more detail the algebraic background and so is giving more insight into the mutual relations between algebra and genetics. Thus, the reader may better understand the main algebraic ideas and methods forming the background for the provided algorithm solving a problem of gene-