Algebraic properties of separated power series

We study the commutative algebra of rings of separated power series over a ring E and that of their extensions: rings of separated (and more specifically convergent) power series from a field K with a separated E-analytic structure. Both of these collections of rings already play an important role in the model theory of non-Archimedean valued fields and we establish their algebraic properties. This will make a study of the analytic geometry over such fields through the classical methods of algebraic geometry possible.     

Algebraic aspects of zariski's equisingularity in codimension 1

In this paper we continue with the study in any characteristic of equisingularity in codimension 1 started in [G-M]. The whclly general concept of equivalent singularities for plane curves introduced in [G-M] and [G-S], allows us to set out equisingularity in codimenson 1 in the case of positive characteristic, even in the non- equicharac-teristic and non-reduced cases. In this situation, we show the natural algebraic properties of equisingularity in codimension 1: good beharvior by monoidal dilatations, equisingularity of all special sections, characterization of the singular locus, etc. We also prove an equisingularity criterion which coincides with Lemma of [A2].     

On semigroup graded PI-algebras

Communicated by L. N. Shevrin     

Groups of automorphisms and PI-algebras

Siberian Mathematical Journal -     

Special power series expansions of monogenic functions around surfaces of codimension two

In this paper we will focus on power series expansions around special surfaces of codimension two, in particular around spheres and products of spheres. This will include a version of the Cauchy–Kowalewski extension theorem around these surfaces. This higher codimension result was only obtained so far in the flat case (see Partial Differential Equations with Complex Analysis. Pitman Research Notes Mathematical Series, vol. 262. Longman Science and Technology: Harlow, 1992; 61–92; Mathematics and its Applications, vol. 53. Kluwer Academic Publishers Group: Dordrecht, 1992). Copyright © 2008 John Wiley & Sons, Ltd.     

Algebraic elements in formal power series rings

We obtain a theorem giving a condition for algebraicity of an element in a formal power series field of characteristicp>0. Using it many results can be proved, for example, the “theorem of the diagonal” of Furstenberg is deduced as an easy corollary. Dedicated to the memory of Chiyo Harase     

Strongly prime algebraic Lie PI-algebras

In a recent paper by the author and Golubkov, it was proved that a strongly prime Lie PI-algebra with an algebraic adjoint representation over an algebraically closed field of characteristic 0 is simple and finite dimensional. In this note, we derive this result from a more general one on strongly prime Lie PI-algebras with abelian minimal inner ideals, which is closely related to the intrinsic characterization of simple finitary Lie algebras with abelian minimal inner ideals.     

Algebraic independence of values of certain Fourier series

The algebraic independence of values of certain Fourier series with algebraic coefficients and their derivatives at algebraic points is proved.     

Algebraic properties of zigzag algebras

Abstract

We give necessary and sufficient conditions for zigzag algebras and certain generalizations of them to be (relative) cellular, quasi-hereditary or Koszul.     

Algebraic properties of Riordan subgroups

Journal of Algebraic Combinatorics - We present properties of the group structure of Riordan arrays. We examine similar properties among known Riordan subgroups, and from this, we define...     

Algebraic properties of Hamel functions

We say that f: ℝ → ℝ is LIF if it is linearly independent over ℚ as a subset of ℝ² and that it is a Hamel function (HF) if it is a Hamel basis of ℝ². We construct an example of HF bijection and use a similar method to prove that any function can be represented as the composition of three HF’s as well as the limit of uniformly convergent sequence of HF’s. Finally we consider products of HF’s, maximal invariant classes (with respect to several algebraic operations) and pose some open problems concerning sets of continuity points of HF’s.     

Algebraic properties of quantum quasigroups

Quantum quasigroups provide a self-dual framework for the unification of quasigroups and Hopf algebras. This paper furthers the transfer program, investigating extensions to quantum quasigroups of various algebraic features of quasigroups and Hopf algebras. Part of the difficulty of the transfer program is the fact that there is no standard model-theoretic procedure for accommodating the coalgebraic aspects of quantum quasigroups. The linear quantum quasigroups, which live in categories of modules under the direct sum, are a notable exception. They form one of the central themes of the paper.From the theory of Hopf algebras, we transfer the study of grouplike and setlike elements, which form separate concepts in quantum quasigroups. From quasigroups, we transfer the study of conjugate quasigroups, which reflect the triality symmetry of the language of quasigroups. In particular, we construct conjugates of cocommutative Hopf algebras. Semisymmetry, Mendelsohn, and distributivity properties are formulated for quantum quasigroups. We classify distributive linear quantum quasigroups that furnish solutions to the quantum Yang-Baxter equation. The transfer of semisymmetry is designed to prepare for a quantization of web geometry.     

Algebraic properties of number theories

Among other things we prove the following. (A) A number theory is convex if and only if it is inductive. (B) No r.e. number theory has JEP. (C) No number theory has AP. We also give some information about the hard cores of number theories.