Some Algebraic Structures with Iteration Lemmata

Manfred Kudlek (Fachbereich Informatik, Universität Hamburg, Germany)

Abstract: This paper deals with solutions of algebraic, linear, and rational systems of equations over an -complete semiring, and their iteration lemmata. These are guaranteed if the underlying structure has an associative multiplicative operation, and its elements have a norm. A number of such structures like words, vectors, traces, trees, graphs, are presented.

Keywords: ω-complete semirings, algebraic, associative structures, iteration lemmata, linear, norm, rational languages, systems of equations