On congruence extension properties for ordered algebras

Abstract

We introduce four extension properties (CEP, QEP, SCEP and SQEP) for ordered algebras, similar to the congruence extension property (CEP) and the strong congruence extension property of usual (unordered) algebras. All four properties turn out to have a description in terms of commutative squares or pullback diagrams. We then use these categorical descriptions to prove an ordered analogue of the well-known relation TP = AP + CEP, namely that a variety of ordered algebras has the ordered transferability property if and only if it has the ordered amalgamation property and QEP.

Homomorphism theorems of ordered semirings

“…Homomorphism theorems for ordered algebras have been investigated by various authors, both from the point of view of ordered algebra and ordered semigroup. Our research is closely related to those which was carried out in [1,2,3,4,5,7]. They defined order-congruence, compatible quasiorder on those structures and investigated further results of homomorphism theorems.…”