Cohomology groups of integral domains and -algebras
Mouadh Akriche, Mohamed Ali Toumi

TL;DR
This paper develops a new homology theory to analyze linear operators in algebraic structures, characterizing integral domains and solving longstanding problems in algebra and operator theory.
Contribution
It introduces a novel homology framework for studying local multipliers and band preserving operators, providing new characterizations of integral domains and solving the Wickstead problem.
Findings
Characterized integral domains where local multipliers are multipliers
Solved the Wickstead problem for Archimedean unital f-algebras
Established a new homology approach for operator analysis
Abstract
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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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Topics in Algebra · Algebraic and Geometric Analysis
