Algebra universalis

, 79:13 | Cite as

Sup-algebra completions and injective hulls of ordered algebras

  • Changchun Xia
  • Bin Zhao


In this paper, we study the \(\sup \)-algebra completions of ordered algebras. Firstly, we show that the \(\sup \)-algebra completions of the ordered algebras \(\mathcal {A}\) are completely determined, up to isomorphism, by the topological nuclei on \(\mathcal {P}(A)\). Moreover, we give the concrete forms of three types of special topological nuclei. Finally, we give the concrete form of injective hulls for arbitrary ordered algebras.


Ordered algebras Sup-algebra completions Injective hulls 

Mathematics Subject Classification

08B30 08C05 06F99 



The authors would like to thank Professor Warren William McGovern and the anonymous reviewer for their valuable comments and suggestions.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShaanxi Normal UniversityXi’anChina

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