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.
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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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Presented by W.Wm. McGovern.
This work is supported by the National Natural Science Foundation of China (11531009) and the Fundamental Research Funds for the Central Universities (GK201501001).
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Xia, C., Zhao, B. Sup-algebra completions and injective hulls of ordered algebras. Algebra Univers. 79, 13 (2018). https://doi.org/10.1007/s00012-018-0501-4
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DOI: https://doi.org/10.1007/s00012-018-0501-4