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The regular-injective envelope of \(S\)-posets

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Abstract

For \(S\) a partially-ordered monoid (pomonoid), in this paper we consider three variations of the notion of essentiality for regular monomorphisms of \(S\)-posets, defining regular-essential, mono-essential and weakly regular-essential extensions of \(S\)-posets. It is shown that, while the last two classes coincide and properly contain the first, they all lead to the same notion of regular-injective envelope. Every \(S\)-poset has such an envelope, and when \(S\) is a pogroup, it may be obtained by letting \(S\) act on the MacNeille completion of the underlying poset.

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Acknowledgments

The authors thank the kind hospitality of Hakim Sabzevari University during the several times we stayed there. We are also grateful to Professor M. Mehdi Ebrahimi and Professor M. Mahmoudi for making a team work in Hakim Sabzevari University and for their attention to this research. We would like to express our gratitude and appreciation to the referee for carefully reading the paper and helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    H. Rasouli

  2. Department of Mathematics, Tafresh University, Tafresh, Iran

    H. Barzegar

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  1. H. Rasouli
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  2. H. Barzegar
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Correspondence to H. Rasouli.

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Communicated by László Márki.

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Rasouli, H., Barzegar, H. The regular-injective envelope of \(S\)-posets. Semigroup Forum 92, 186–197 (2016). https://doi.org/10.1007/s00233-015-9691-7

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  • DOI: https://doi.org/10.1007/s00233-015-9691-7

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