ERRATUM: "ITERATION ALGEBRAS"

On Algebras with Iteration

Several concepts of algebras with solutions of recursive equation systems are compared: CPO-enrichable algebras are proved to be iteration algebras of Z. Ésik, and iteration algebras are a special case of the recently introduced Elgot algebras (which are the monadic algebras for the free iterative monad). Another special case of iteration algebras are the iterative algebras of E. Nelson and J. ...

Iteration theories as monadic algebras

Iteration theories, as introduced by Stephen Bloom and Zoltán Ésik, are Lawvere theories equipped with a function assigning to every morphism e : n → n + k (representing a system of n recursive equations whose left-hand sides are variables and right-hand sides are terms in those n variables and k parameters) a morphism e† : n → k (representing a solution of those equations). This function is re...

Iteration of Quadratic Maps on Matrix Algebras

ALEXANDRA NASCIMENTO BAPTISTA Department of Mathematics, School of Technology and Management, Polytechnic Institute of Leiria, Campus 2, Morro do Lena – Alto do Vieiro, 2411-901, Leiria, Portugal Centro de Investigação em Matemática e Aplicações, University of Évora, Rua Romão Ramalho, 59, 7000-671, Évora, Portugal CARLOS CORREIA RAMOS Centro de Investigação em Matemática e Aplicações, Departme...

Iteration Algebras are not Finitely Axiomatizable : Extended

Algebras whose underlying set is a complete partial order and whose termoperations are continuous may be equipped with a least fixed point operation μx.t. The set of all equations involving the μ-operation which hold in all continuous algebras determines the variety of iteration algebras. A simple argument is given here reducing the axiomatization of iteration algebras to that of Wilke algebras...

Erratum