Geodesic
Pseudocomplements in sum-ordered partial semirings
Discussiones Mathematicae. General Algebra and Applications, Tome 27 (2007) no. 2, pp. 169-186

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We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several well-known elementary characteristics of Stone algebras have analogues for such semirings.
Keywords: Glivenko theorem, partial monoid, partial semiring, pseudocomplementation, semigroup, Stone semiring, sum-ordering 
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Cīrulis, Jānis. Pseudocomplements in sum-ordered partial semirings. Discussiones Mathematicae. General Algebra and Applications, Tome 27 (2007) no. 2, pp. 169-186. http://geodesic.mathdoc.fr/item/DMGAA_2007_27_2_a1/