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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1125,
author = {J\=anis C\=\i rulis},
title = {Pseudocomplements in sum-ordered partial semirings},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {27},
year = {2007},
pages = {169-186},
zbl = {1138.06007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1125}
}
Jānis Cīrulis. Pseudocomplements in sum-ordered partial semirings. Discussiones Mathematicae - General Algebra and Applications, Tome 27 (2007) pp. 169-186. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1125/
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