On Mono- and Epimorphisms in Varieties of Ordered Algebras

Abstract

We study morphisms in varieties of ordered universal algebras. We prove that (i) monomorphisms are precisely the injective homomorphisms and that (ii) every regular monomorphism is an order embedding, but the converse is not true in general. We also give a necessary and sufficient condition for a morphism to be a regular epimorphism. Finally, we discuss factorizations in such varieties.

Key Words:

• Directed kernel
• Extremal epimorphism
• Extremal monomorphism
• Factorization
• Ordered algebra
• Order-congruence
• Regular epimorphism
• Regular monomorphism

2010 Mathematics Subject Classification:

• Primary: 06F99
• 18A20
• Secondary: 08B25

ACKNOWLEDGMENT

We are very grateful to the referee whose valuable suggestions helped to improve this paper.

Notes

Communicated by V. Gould.