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Notes on mildly distributive semilattices

  • Sergio Arturo Celani EMAIL logo and Luciano Javier González
From the journal Mathematica Slovaca

Abstract

In this paper we shall investigate the mildly distributive meet-semilattices by means of the study of their filters and Frink-ideals as well as applying the theory of annihilator. We recall some characterizations of the condition of mildly-distributivity and we give several new characterizations. We prove that the definition of strong free distributive extension, introduced by Hickman in 1984, can be simplified and we show a correspondence between (prime) Frink-ideals of a mildly distributive semilattice and (prime) ideals of its strong free distributive extension.


This work was supported by CONICET Grant No. PIP 112-201101-00636.



(Communicated by Miroslav Ploščica)


Acknowledgement

We greatly appreciate the comments and suggestions of a referee that helped to improve the paper.

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Received: 2015-4-20
Accepted: 2016-5-18
Published Online: 2017-9-22
Published in Print: 2017-10-26

© 2017 Mathematical Institute Slovak Academy of Sciences

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