TL;DR
This paper extends the concept of Henselian pairs to noncommutative algebra, demonstrating that such pairs with certain topological properties possess Henselizations on both sides, thus broadening the theoretical framework.
Contribution
It introduces the notion of noncommutative Henselizations and proves their existence for Hausdorff pairs in this setting, expanding classical algebraic concepts.
Findings
Noncommutative Henselizations exist for Hausdorff pairs.
Extension of Henselian pair theory to noncommutative algebra.
Establishment of existence results for noncommutative Henselizations.
Abstract
In this paper, the familiar notion of a Henselian pair is extended to the noncommutative case. Furthermore, the problem of Henselizations is studied in the noncommutative context, and it is shown that every (not necessarily commutative) pair which is Hausdorff with respect to a certain topology has a left (and right) Henselization.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Advanced Algebra and Geometry