Existence of pseudo-superinvolutions of the first kind.
Explicit expression of Cartan’s connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere
We study effectively the Cartan geometry of Levi-nondegenerate C 6-smooth hypersurfaces M 3 in ℂ2. Notably, we present the so-called curvature function of a related Tanaka-type normal connection explicitly in terms of a graphing function for M, which is the initial, single available datum. Vanishing of this curvature function then characterizes explicitly the local biholomorphic equivalence of such M 3 ⊂ ℂ2 to the Heisenberg sphere ℍ3, such M’s being necessarily real analytic.
Exponentiation de la dérivation, et intégration des séries en variables non commutatives
Ext-algebras and derived equivalences
Using derived categories, we develop an alternative approach to defining Koszulness for positively graded algebras where the degree zero part is not necessarily semisimple.
Extending Derivations and Endomorphisms to Skew Polynomial Rings
Extending Group Modules in a Relatively Prime Case.
Extension-closure and attainability for varieties of algebras with involution
Extensions of Chain Rings.
Extensions of rational modules.
-derivations on rings and modules
If is a hereditary torsion theory on and is the localization functor, then we show that every -derivation has a unique extension to an -derivation when is a differential torsion theory on . Dually, it is shown that if is cohereditary and is the colocalization functor, then every -derivation can be lifted uniquely to an -derivation .
-radical extensions of rings
Faithfully quadratic rings - a summary of results
This is a summary of some of the main results in the monograph Faithfully Ordered Rings (Mem. Amer. Math. Soc. 2015), presented by the first author at the ALANT conference, Będlewo, Poland, June 8-13, 2014. The notions involved and the results are stated in detail, the techniques employed briefly outlined, but proofs are omitted. We focus on those aspects of the cited monograph concerning (diagonal) quadratic forms over preordered rings.
Fastgeordnete und geordnete lokale Ringe und ihre geometrische Anwendung
Filtrations, Stable Clifford Theory and Group-Graded Rings and Modules.
Finite automata and algebraic extensions of function fields
We give an automata-theoretic description of the algebraic closure of the rational function field over a finite field , generalizing a result of Christol. The description occurs within the Hahn-Mal’cev-Neumann field of “generalized power series” over . In passing, we obtain a characterization of well-ordered sets of rational numbers whose base expansions are generated by a finite automaton, and exhibit some techniques for computing in the algebraic closure; these include an adaptation to positive...
Finite morphisms between differentiable algebras.
First order calculi with values in right-universal bimodules
The purpose of this note is to show how calculi on unital associative algebra with universal right bimodule generalize previously studied constructions by Pusz and Woronowicz [1989] and by Wess and Zumino [1990] and that in this language results are in a natural context, are easier to describe and handle. As a by-product we obtain intrinsic, coordinate-free and basis-independent generalization of the first order noncommutative differential calculi with partial derivatives.
Flat and projective modules.
Fonctions continues et séparément additives
Forms of Hopf algebras and Galois theory