Infinite Lexicographic Products of Triangular Algebras
S. C. Power
TL;DR
This paper explores the relationship between linear orderings and triangular operator algebras, introducing a lexicographic product for these algebras and analyzing the Jacobson radical in infinite cases.
Contribution
It defines a lexicographic product for triangular operator algebras and determines the Jacobson radical for infinite products of upper triangular matrix algebras.
Findings
Established a new connection between orderings and operator algebras
Defined a lexicographic product for triangular operator algebras
Determined the Jacobson radical for infinite lexicographic products
Abstract
Some new connections are given between linear orderings and triangular operator algebras. A lexicograhic product is defined for triangular operator algebras and the Jacobson radical of an infinite lexicographic product of upper triangular matrix algebras is determined.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Topics in Algebra · Advanced Algebra and Logic