Injective hulls for ordered algebras
We study the injectivity of ordered algebras with respect to the class of homomorphisms that are order-embeddings and one more class of morphisms. We do this in the category where morphisms need not be homomorphisms, but satisfy a condition which is weaker than operation-preservation. In this setting, the injective objects turn out to be precisely sup-algebras. We also show how to construct injective hulls of ordered algebras satisfying certain conditions.
Key words and phrasesordered algebra sup-algebra injectivity injective hull
2010 Mathematics Subject ClassificationPrimary: 08B30 Secondary: 08C05 06F99
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