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Algebra universalis

, 79:13 | Cite as

Sup-algebra completions and injective hulls of ordered algebras

  • Changchun Xia
  • Bin Zhao
Article
  • 58 Downloads

Abstract

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.

Keywords

Ordered algebras Sup-algebra completions Injective hulls 

Mathematics Subject Classification

08B30 08C05 06F99 

Notes

Acknowledgements

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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