Algebra universalis

, Volume 76, Issue 3, pp 339–349 | Cite as

Injective hulls for ordered algebras

  • Xia Zhang
  • Valdis Laan


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 phrases

ordered algebra sup-algebra injectivity injective hull 

2010 Mathematics Subject Classification

Primary: 08B30 Secondary: 08C05 06F99 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesSouth China Normal UniversityGuangzhouChina
  2. 2.Department of MathematicsSouthern Illinois University CarbondaleCarbondaleUSA
  3. 3.Institute of MathematicsUniversity of TartuTartuEstonia

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