整环的上同调群与-代数
Cohomology groups of integral domains and -algebras
摘要：
本文介绍一种新的同调理论，用于研究局部乘子和保带算子等线性算子。我们的想法是研究消失的同调问题。这使我们能够刻画其中任何局部乘子都是乘子的整环，这部分地回答了R. V. Kadison [J. Algebra 130，No.2，（1990）494 - 509].最后，我们解决了阿基米德酉f-代数类的Wickstead问题[Compositio Math，35（3）（1977），225 - 238]。
英文摘要：
In this paper, we introduce a new homology theory devoted to the study of linear operators such as local mutipliers and band preserving operators. The idea is to study the vanishing homology problem. This enables us to characterize integral domains in which any local multiplier is a multiplier, which gives a partial answer to a problem posed by R. V. Kadison [J. Algebra 130, No.2, (1990) 494-509]. Finally, we solve the Wickstead problem [Compositio Math, 35(3) (1977), 225--238] for the class of Archimedean unital f-algebras.
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