Multi-algebra duplication (Q1111972)

The aim of this paper is to use multi-algebra duplication to simplify the proofs of \textit{J. Lopez-Sanchez}, and \textit{A. Perez de Vargas} [Bull. Math. Biol. 47, 771-782 (1985; Zbl 0586.92016)], and to show that this idea can be usefully applied to other situations. The author starts, however, with a brief, but very lucid introduction to some of the basic algebraic ideas in genetics - this should prove very useful to readers not very familiar with this subject. For a full account of algebra in genetics he rightly refers the reader to \textit{A. Wörz-Busekros} [Algebras in genetics. Lect. Notes in Biomathematics 36 (1980; Zbl 0431.92017)]. Multi-algebra duplication of two algebras having a common basis is defined in terms of the duplication of either algebra [see the author's paper, Proc. Edinburgh Math. Soc., II. Ser. 17, 289-298 (1971; Zbl 0247.92002)], and his two main theorems are concerned with subalgebras of such a duplication, and the train roots. [In Theorem 1, the first lower case ``c'' should be replaced by an upper case ``C''.]