Том 234, № 2 (2018)
- Жылы: 2018
- Мақалалар: 16
- URL: https://journals.rcsi.science/1072-3374/issue/view/14956
Article
In Memory of S. A. Evdokimov
On the Reduced Group of Principal Units in Cyclic Extensions of Local Fields
Аннотация
The reduced group of principal units of cyclic extensions of local fields is considered as a Galois module. This module is studied by examining the Jordan canonical form of the generating automorphism of the Galois group.
On a Strange Homotopy Category
Аннотация
Let \( \mathcal{C} \) be an additive category in which each morphism has a kernel. It is proved that the homotopy category of the category of complexes over \( \mathcal{C} \) which are concentrated in degrees 2, 1, 0 and are exact in degrees 2 and 1 is Abelian. Under assumption that a category \( \mathcal{C} \) is Abelian, this result was obtained earlier by considering the heart of a suitable t-structure on the homotopy category of \( \mathcal{C} \).
Full and Elementary Nets over the Quotient Field of a Principal Ideal Ring
Аннотация
Let K be the quotient field of a principal ideal ring R, and let σ = (σij) be a full (respectively, elementary) net of order n ≥ 2 (respectively, n ≥ 3) over K such that the additive subgroups σij are nonzero R-modules. It is proved that, up to conjugation by a diagonal matrix, all σij are ideals of a fixed intermediate subring P, R ⊆ P ⊆ K.
Construction of a Cyclic Extension of Degree p2 for a Complete Field
Аннотация
The aim of the paper is to construct an embedding of a given cyclic extension of degree p of a complete discrete valuation field of characteristic 0 with an arbitrary residue field of characteristic p > 0 into a cyclic extension of degree p2. The result extends the construction obtained by S. V. Vostokov and I. B. Zhukov in terms of Witt vectors, to a wider interval of values for the ramification jump of the original field extension.
On Biorthogonal p-Adic Wavelet Bases
Аннотация
Dual p-adic multiresolution analyses (MRAs) generated by scaling test functions are studied. It is proved that if two MRAs are dual, then each of them is the Haar MRA. A characterization of all biorthogonal wavelet systems associated with the Haar MRA is given for the case p = 2.
On T-Amorphous Association Schemes
Аннотация
An association scheme is said to be T-amorphous if it is antisymmetric and any tournament obtained by an appropriate merging of its classes is doubly regular. The goal of this paper is to study basic properties of T-amorphous schemes.
The Normalizer of the Elementary Linear Group of a Module Arising when the Base Ring is Extended
Аннотация
Let S be a commutative ring with 1 and R a unital subring. Let M be a free S-module of rank n ≥ 3. In 1994, V. A. Koibaev described the normalizer of AutS(M) in the group AutR(M). In the present paper, it is proved that the normalizer of the elementary linear group E????(M) in AutR(M) coincides with that of AutS(M), namely, NAutR(M)(E????(M)) = Aut(S/R)⋉AutS(M). If S is free of rank m as an R-module, then NGL(mn,R)(E(n, S)) = Aut(S/R)⋉GL(n, S). Moreover, for any proper ideal A of R,
The Restrictions of Representations of the Special Linear Group to Subsystem Subgroups of Type A2
Аннотация
The restrictions of irreducible representations of the special linear group over an algebraically closed field of positive characteristic p to subsystem subgroups of type A2 are studied. The composition factors for such restrictions are described in the case where the highest weights of the representations are locally small.
Testing Isomorphism of Central Cayley Graphs Over Almost Simple Groups in Polynomial Time
Аннотация
A Cayley graph over a group G is said to be central if its connection set is a normal subset of G. It is proved that for any two central Cayley graphs over explicitly given almost simple groups of order n, the set of all isomorphisms from the first graph onto the second can be found in time poly (n).
Nonclassical Birational Models for Spec ℚ
Аннотация
Generalized subrings of the ring of integers that give birational models for the field of rationals are studied. A homogeneous strengthening of Evdokimov’s theorem is proved. An approach to calculation of homotopy groups with the help of generalized rings is proposed.
Tamaschke’s Results on Schur Rings and a Generalization of Association Schemes
Аннотация
The concepts of an association scheme and a coherent configuration are generalized by analyzing a relationship between S-rings (Schur rings) and association schemes. In this connection, Tamaschke’s results on S-rings and other generalizations of association schemes are discussed.
Subgroups of the General Linear Group That Contain Elementary Subgroup Over a Rank 2 Commutative Ring Extension
Аннотация
Let R = \( \prod \limits_{i\in I}{F}_i \) be the direct product of fields, and let\( S=R\left[\sqrt{d}\right]=\prod \limits_{i\in I}{F}_i\left[\sqrt{d_i}\right] \) be a rank 2 extension of R. The subgroups of the general linear group GL(2n,R), n ≥ 3, that contain the elementary group E (n, S) are described. It is shown that for every such a subgroup H there exists a unique ideal A ⊴ R such that E (n, S)E(2n,R,A) ≤ H ≤ NGL(2n,R) (E (n, S)E(2n,R,A)).