Abstract of Paper

Formal Series over Algebras
by Werner Kuich


We define two types of series over $\Sigma$-algebras: formal series and, as
a special case, term series. By help of term series we define systems (of
equations) that have tuples of formal series as solutions. We then introduce
finite automata and polynomial systems and show that they are mechanisms of
equal power. Morphisms from formal series into power series yield
combinatorial results. Moreover, we generalize the Kleene Theorem.