Homological algebra and set theory
Homological algebra and set theory
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DOI：
10.1090/s0002-9947-1977-0453520-x
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发表时间：
1977-03
影响因子：
1.3
通讯作者：
P. Eklof
中科院分区：
文献类型：
--
作者：
P. Eklof
。假设可构造性公理，给出全局维数为1的环A的Ext\消失的充分必要条件。利用马丁公理，证明这些条件的必要性不是ZFC定理。给出了阿贝尔群理论的应用，包括关于阿贝尔群分裂的贝尔问题的部分解决方案（假设 V = L）。阿贝尔群论中的一些独立性结果也得到了证明。
. Assuming the Axiom of Constructibility, necessary and sufficient conditions are given for the vanishing of Ext\ for rings A of global dimension 1. Using Martin's Axiom, the necessity of these conditions is shown not to be a theorem of ZFC. Applications are given to abelian group theory, including a partial solution (assuming V = L) to a problem of Baer on the splitting of abelian groups. Some independence results in abelian group theory are also proved.