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Wehrung, Friedrich

We construct a completely normal bounded distributive lattice D in which for every pair (a, b) of elements, the set {x ∈ D | a ≤ b ∨ x} has a countable coinitial subset, such that D does not carry any binary operation - satisfying the identities x ≤ y ∨(x-y),(x-y)∧(y-x) = 0, and x-z ≤ (x-y)∨(y-z). In particular, D is not a homomorphic image of the ...

Caillot, J. F. Wehrung, F.
Published in
Semigroup Forum

(i) A partially ordered abelian group G is finitely presented if and only if G is finitely generated as a group, G+ is well-founded as a partially ordered set, and the set of minimal elements of G+\ {0} is finite. (ii) Torison-free, finitely presented partially ordered abelian groups can be represented as subgroups of some Zn, with a finitely gener...

Wehrung, Friedrich

We extend the usual deﬁnition of coherence, for modules over rings, to partially ordered right modules over a large class of partially ordered rings, called po-rings. In this situation, coherence is equivalent to saying that solution sets of ﬁnite systems of inequalities are ﬁnitely generated semimodules. Coherence for ordered rings and modules, wh...