On permutation polynomials over finite fields.
On p-groups as Galois groups.
On places of algebraic function fields.
On polynomial transformations
On polynomial transformations II
On polynomial transformations in several variables
On Polynomials and Exponential Polynomials in Several Complex Variables.
On polynomials taking small values at integral arguments II
On polynomials with flat squares
On preordered fields related to Hilbert's 17th problem.
On products of additive functions (a third approach).
On prosolvable subgroups of profinite free products and some applications.
On quasi-ideals of semirings.
On quotients of the space of orderings of the field ℚ(x)
In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings - it is, in general, nontrivial to determine whether, for a subgroup the derived quotient structure is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.
On rank of extensions of valuations
On Real Local-Global Principles.
On realizability of p-groups as Galois groups
2000 Mathematics Subject Classification: 12F12, 15A66.In this article we survey and examine the realizability of p-groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of such a group as a Galois group, the embedding problem (i.e., realizability over a given subextension), descriptions of such extensions, automatic realizations among p-groups, and related topics.
On reducible trinomials [Book]
On Relations Between Zeros of Galois Polynomials.
On relative integral bases for unramified extensions
0. Introduction. Since ℤ is a principal ideal domain, every finitely generated torsion-free ℤ-module has a finite ℤ-basis; in particular, any fractional ideal in a number field has an "integral basis". However, if K is an arbitrary number field the ring of integers, A, of K is a Dedekind domain but not necessarily a principal ideal domain. If L/K is a finite extension of number fields, then the fractional ideals of L are finitely generated and torsion-free (or, equivalently, finitely generated and...