Advances and Applications in Discrete Mathematics
Volume 15, Issue 1, Pages 75 - 90
(January 2015) http://dx.doi.org/10.17654/AADMJan2015_075_090 |
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COUNTABLE LOWER SEMILATTICES WHOSE SET OF JOIN-REDUCIBLE ELEMENTS IS WELL-ORDERED
Hamid Kulosman and Alica Miller
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Abstract: In our previous papers [2] and [3], we have introduced the notion of special semigroups. They are commutative Boolean semigroups that can be built from a trivial semigroup in finitely or infinitely many steps, where in each step an idempotent is adjoined in one of the three allowed ways. In our paper [4], we characterized finite special semigroups. In this paper, we show that some countable special semigroups correspond to the lower semilattices whose set of join-reducible elements is well-ordered. In that way, we characterize these lattices. |
Keywords and phrases: Boolean semigroup, adjoining idempotents, special semigroup, lower semilattice, join-reducible element. |
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