Pseudocomplements in sum-ordered partial semirings. (English) Zbl 1138.06007
The paper deals with ordered semigroups and semirings. The author characterizes the so-called \(g\)-semigroups, i.e., pseudocomplemented semigroups such that their sets of pseudocomplements are Boolean algebras. Further he investigates sum-ordered partially additive semirings with the property that their multiplicative reducts are \(g\)-semigroups.
Reviewer: Jiří Rachůnek (Olomouc)
MSC:
06F25 | Ordered rings, algebras, modules |
06D15 | Pseudocomplemented lattices |
06F05 | Ordered semigroups and monoids |
08A55 | Partial algebras |
16Y60 | Semirings |