Solutions principales et rang d'un système d'équations avec constantes dans le monoide libre (Q797700)

In order to give a far-reaching common generalization of Lentin's and Makanin's results concerning equations without and with constants, the author defines a system of equations over a finite alphabet \(E\cup C (E\cap C=\emptyset)\) to be a set of quadruples \((e_ i,e'\!_ i,E,C)\), \(e_ i,e'\!_ i\in(E\cup C)^*\), and a solution of this system to be a morphism \(\alpha:(E\cup C)^*\to(A\cup C)^*\) where A is arbitrary finite such that \(A\cap C=\emptyset\), \(\alpha\) acts identically on C, and \(\alpha e_ i=\alpha e'\!_ i\). All essential results carry over to this case. In particular, every solution can be derived from a unique principal solution, and the calculation of the latter ones is equivalent (at least in the case of a finite system) to finding the principal solutions of some single equation of the same rank. Thus, the rank of a system can be determined, too.