The aim of the paper is to investigate the partial semiring C ∞+ (X) of all continuous functions on a topological space X that take values in the semiring [0, ∞] with the usual topology. Maximal ideals of the partial semiring C ∞+ (X) are studied, and fundamental properties of its prime ideals are described.
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...
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