6533b7d6fe1ef96bd1266ea9

RESEARCH PRODUCT

Pseudocomplements in sum-ordered partial semirings

Janis Cirulis

subject

Class (set theory)Algebra and Number TheorySemigroupApplied MathematicsBoolean algebra (structure)Multiplicative functionZero (complex analysis)Type (model theory)SemiringKleene algebraCombinatoricssymbols.namesakesymbolsComputer Science::Formal Languages and Automata TheoryMathematics

description

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.

https://doi.org/10.7151/dmgaa.1125