Countably Generated Matrix Algebras
Arvid Siqveland

TL;DR
This paper introduces a new way to complete associative algebras in the context of modules, linking it to deformation theory and formal algebra constructions, with applications to noncommutative deformation functors.
Contribution
It defines a novel completion process for associative algebras in module sets, connecting it to GMMP-algebras and deformation theory, providing a unique prorepresenting hull.
Findings
Defines completion of associative algebras in modules
Links completion to GMMP-algebras and deformation functors
Establishes uniqueness of the formal algebra hull
Abstract
We define the completion of an associative algebra in a set of right -modules in such a way that if is an ideal in a commutative ring the completion in the (right) module is This works by defining as a formal algebra determined up to a computation in a category called GMMP-algebras. From deformation theory we get that the computation results in a formal algebra which is the prorepresenting hull of the noncommutative deformation functor, and this hull is unique up to isomorphism.
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Taxonomy
TopicsAdvanced Algebra and Logic · Computability, Logic, AI Algorithms · Rings, Modules, and Algebras
