We study fixed point problem for boolean algebras with an endomorphism operator k. In particular we prove that in every finite algebra of this kind there exist polynomials f (x) (in which x only occurs within the scope of k) without fixed point. Some examples of Boolean algebras with endomorphism operator k in which every polynomial f (x) (in which x only occurs within the scope of k) has a fixed point are also given. Also we establish some properties of the algebras of this kind.
A note on the fixed point for the polynomials of a boolean algebra with an operator of endomorphism
GNANI, Giuliana;MAZZANTI, Giuliano
1999
Abstract
We study fixed point problem for boolean algebras with an endomorphism operator k. In particular we prove that in every finite algebra of this kind there exist polynomials f (x) (in which x only occurs within the scope of k) without fixed point. Some examples of Boolean algebras with endomorphism operator k in which every polynomial f (x) (in which x only occurs within the scope of k) has a fixed point are also given. Also we establish some properties of the algebras of this kind.File in questo prodotto:
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