On ordered divisible groups
نویسندگان
چکیده
منابع مشابه
On Ordered Divisible Groupso)
Introduction and remarks. In the theory of r)a-sets three main theorems stand out: that an r/0-set is universal for totally ordered sets of power not exceeding Xa, that any two 7/a-sets of power Na are isomorphic and that 7/a-sets of power Xa exist provided Ka is a regular cardinal number and 2~2i<<> 2t*sS&a. L. Gillman and M. Jerison [6] have shown that a real closed (totally ordered) field wh...
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We show that a large class of divisible abelian `-groups (lattice ordered groups) of continuous functions is interpretable (in a certain sense) in the lattice of the zero sets of these functions. This has various applications to the model theory of these `-groups, including decidability results.
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The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the tr...
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Introduction. A p-divisible group X can be seen as a tower of building blocks, each of which is isomorphic to the same finite group scheme X[p]. Clearly, if X1 and X2 are isomorphic then X1[p] ∼= X2[p]; however, conversely X1[p] ∼= X2[p] does in general not imply that X1 and X2 are isomorphic. Can we give, over an algebraically closed field in characteristic p, a condition on the p-kernels whic...
متن کاملNOTES ON TATE’S p-DIVISIBLE GROUPS
The aim here is simply to provide some details to some of the proofs in Tate's paper [T]. 2. Tate's Section 2.2 2.1. Lemmas about divisibility. We say Γ → Γ is an isogeny of the formal group Γ = Spf(A) if the corresponding map A → A is injective and makes A free over itself of finite rank. Tate calls Γ divisible, if p : Γ → Γ is an isogeny. This is equivalent to ψ : A → A is injective and makes...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1960
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1960-0140595-8