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首页> 外文期刊>Communications in Contemporary Mathematics >RATIONAL POLYHEDRA AND PROJECTIVE LATTICE-ORDERED ABELIAN GROUPS WITH ORDER UNIT
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RATIONAL POLYHEDRA AND PROJECTIVE LATTICE-ORDERED ABELIAN GROUPS WITH ORDER UNIT

机译：有序单元的有理多面体和射影格有序的阿贝尔群

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摘要

An u0001-group G is an abelian group equipped with a translation invariant lattice-order.nBaker and Beynon proved that G is finitely generated projective if and only if it isnfinitely presented. A unital u0001-group is an u0001-group G with a distinguished order unit,ni.e. an element 0 ≤ u ∈ G whose positive integer multiples eventually dominate everynelement of G. Unital u0001-homomorphisms between unital u0001-groups are group homomorphismsnthat also preserve the order unit and the lattice structure. A unital u0001-groupn(G, u) is projective if whenever ψ : (A, a) → (B, b) is a surjective unital u0001-homomorphismnand φ : (G, u) → (B, b) is a unital u0001-homomorphism, there is a unital u0001-homomorphismnθ : (G, u) → (A, a) such that φ = ψ ◦ θ. While every finitely generated projective unitalnu0001-group is finitely presented, the converse does not hold in general. Classical algebraicntopology (`a la Whitehead) is combined in this paper with the Wu0001lodarczyk–Morellinsolution of the weak Oda conjecture for toric varieties, to describe finitely generatednprojective unital u0001-groups
机译：一个u0001群G是一个配备了平移不变格序的阿贝尔群.nBaker和Beynon证明了当且仅当它无限地存在时，它是有限生成的射影。单位u0001-group是具有专有顺序单位ni.e的u0001-groupG。元素0≤u∈G，其正整数倍数最终决定G的所有元素。单位u0001-组之间的单位u0001同态是组同态n，它也保留了阶数单位和晶格结构。如果只要ψ：（A，a）→（B，b）是形容词单位u0001-同态n和φ：（G，u）→（B，b）是单位，则u0001-groupn（G，u）就是单位射影u0001同态，存在一个统一的u0001同态nθ：（G，u）→（A，a）使得φ=ψ◦θ。虽然每个有限生成的射影unitalnu0001-group都是有限表示的，但一般而言并非相反。本文将经典代数拓扑学（“ a la Whitehead”）与复曲面变体的弱Oda猜想的Wu0001lodarczyk–Morellin解结合，以描述有限生成的投影单位u0001-群

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