Some properties of retract lattices of monounary algebras

Mathematica Slovaca

Danica Jakubíková-Studenovská¹  Jozef Pócs¹ 

关键词: monounary algebra;    retract;    retract lattice;   

DOI  :  10.2478/s12175-012-0002-4

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R ∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of R ∅(A, f) are characterized. Further, there are described all connected monounary algebras (A, f) such that the lattice R ∅(A, f) is complemented. In this case R ∅(A, f) forms a boolean lattice.

【 授权许可】

Unknown