2024/08/02 by Siqveland, Arvid · 3 citations
#14A22 #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2408.01034
We define the completion of an associative algebra A in a set M=\M1,…,Mr\ of r right A-modules in such a way that if \mathfrak a⊆ A is an ideal in a commutative ring A the completion A in the (right) module A/\mathfrak a is AM≃ A\mathfrak a. This works by defining AM 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.