As we have seen in Chapter 2, the dynamics of the space of representations of our algebra
A, ie the dynamics of the space of measurements of the family of observables ξ that A is …

We make some remarks on deformation theory over non-commutative base. We describe
the base algebra of semi-universal non-commutative deformations using vector spaces T 1 …

We prove that for an arbitrary field $ k, $ a complete, associative $ k^ r $-algebra $\hat H $
augmented over $ k^ r $ has exactly $ r $ maximal two-sided ideals and deserves the name …

We define the completion of an associative algebra $ A $ in a set $ M=\{M_1,\dots, M_r\} $ of
$ r $ right $ A $-modules in such a way that if $\mathfrak a\subseteq A $ is an ideal in a …

This is our second scope of the consideration on the corresponding topologization and the
corresponding functional analytification. We will focus on the corresponding functorial and …

In this dissertation, we discuss mainly the corresponding geometric and representation
theoretic aspects of relative p-adic Hodge theory and p-adic motives. To be more precise …

We extend the classical concept of deformation of an associative algebra, as introduced by
Gerstenhaber, by using monoidal linear categories and cocommutative coalgebras as …

This paper introduces arithmetic geometry for polynomial identity algebras using non-
commutative (formal) deformation theory. Since formal deformation theory is inherently local …

This book is written to make the audience competent to read the book Mathematical Models
in Science by OA Laudal (Laudal, 2021). That book is based on noncommutative algebraic …

We give a definition of associative schemes, schemes of associative rings, over a field $ k, $
using the definition of completion of an associative $ k $-algebra in a finite set of simple …