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Injective Hulls in the Category of Mildly Distributive Semilattices

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Abstract

The main purpose of this paper is to study the injectivity in the category of mildly distributive semilattices, which will generalize the related results in the category of distributive lattices given by Balbes and Banaschewski & Bruns respectively. Concretely, we shall show that the \({\mathscr{M}}\)-injective objects in the category of mildly distributive semilattices are precisely complete Boolean algebras and every mildly distributive semilattice has an \({\mathscr{M}}\)-injective hull. As corollaries, the above results also hold in the category of distributive semilattices.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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  1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710129, People’s Republic of China

    Changchun Xia

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  1. Changchun Xia
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Correspondence to Changchun Xia.

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This work is supported by the National Natural Science Foundation of China (12101497) and the Fundamental Research Funds for the Central Universities (G2020KY05206).

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Xia, C. Injective Hulls in the Category of Mildly Distributive Semilattices. Order 39, 381–388 (2022). https://doi.org/10.1007/s11083-021-09584-1

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