The Strong Endomorphism Kernel Property in Ockham Algebras

Abstract

An endomorphism on an algebra 𝒜 is said to be “strong” if it is compatible with every congruence on 𝒜; and 𝒜 is said to have the “strong endomorphism kernel property” if every congruence on 𝒜, different from the universal congruence, is the kernel of a strong endomorphism on 𝒜. Here we consider this property in the context of Ockham algebras. In particular, for those MS-algebras that have this property we describe the structure of their dual space in terms of 1-point compactifications of discrete spaces.

Key Words:

• Endomorphism kernel
• Ockham algebra
• 1-point compactification

1991 Mathematics Subject Classification:

• 06D30

Notes

Communicated by V. Gould.