Abstract
AbstractWe examine the problem of projecting subsets of a commutative, positively ordered monoid into an o-ideal. We prove that to this end one may restrict to a sufficient subset, for whose cardinality we provide an explicit upper bound. Several applications to set functions, vector lattices and other more explicit structures are provided.
Funder
Università degli Studi di Milano - Bicocca
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Reference15 articles.
1. Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Springer, Dordrecht (2006)
2. Anderson, D.D., Johnson, E.W.: Ideal theory in commutative semigroups. Semigroup Forum 30, 127–158 (1984)
3. Birkhoff, G.: Lattice Theory. Amer. Math. Soc. Colloquium Publications, vol. 25. American Mathematical Society, Providence, RI, (1973)
4. Blyth, T.S.: Lattices and Ordered Algebraic Structures. Springer, London (2006)
5. Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1954)