Abstract
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.
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05 November 2021
A Correction to this paper has been published: https://doi.org/10.1007/s00012-021-00749-y
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Presented by W. McGovern.
Research of the first named author was supported by Natural Science Foundation of Guangdong Province, China (no. 2016A030313832) and the Science and Technology Program of Guangzhou, China (no. 201607010190). Research of the second named author was supported by institutional research funding IUT20-57 of the Estonian Ministry of Education and Research; support from the exchange agreement between the Estonian and the Hungarian Academies of Sciences is also gratefully acknowledged.
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Zhang, X., Laan, V. Injective hulls for ordered algebras. Algebra Univers. 76, 339–349 (2016). https://doi.org/10.1007/s00012-016-0404-1
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DOI: https://doi.org/10.1007/s00012-016-0404-1