Open Access
Access granted
Subscription Access
Vol 55, No 1 (2016)
- Year: 2016
- Articles: 10
- URL: https://journal-vniispk.ru/0002-5232/issue/view/14535
Article
1-8
Dynamic Mereotopology. III. Whiteheadian Type of Integrated Point-Free Theories of Space and Time. II
Abstract
This is the second in a three-part series of papers shortly denoted by Part I [1], and Part III (Algebra and Logic, 55, No. 3). The papers mentioned are devoted to some Whiteheadian theories of space and time. Part I contains a historical introduction and some facts from static mereotopology. The present Part II introduces a point-based definition of dynamic model of space and standard dynamic contact algebra based on the so-called snapshot construction. This model has an explicit time structure with an explicit set of time points equipped with a before-after relation and a set of regions changing in time, called dynamic regions. The dynamic model of space contains several definable spatio-temporal relations between dynamic regions: space contact, time contact, precedence, and some others. We prove a number of statements for these relations, which in Part III are taken as axioms for the abstract definition of some natural classes of dynamic contact algebras, considered as an algebraic formalization of dynamic mereotopology.
9-23
Definability of Linear Orders over Negative Equivalences
Abstract
We study linear orders definable over negative and positive equivalences and their computable automorphisms. Special attention is paid to equivalences like η(α) = α2∪idω, α ⊆ ω. In particular, we describe orders that have negative presentations over such equivalences for co-enumerable sets α. Presentable and nonpresentable order types are exemplified for equivalences with various extra properties. We also give examples of negative orders with computable automorphisms whose inverses are not computable.
24-37
The Schur–Wielandt Theory for Central S-Rings
Abstract
Two basic results on S-rings over an Abelian group are the Schur theorem on multipliers and the Wielandt theorem on primitive S-rings over groups with a cyclic Sylow subgroup. Neither of these is directly generalized to the non-Abelian case. Nevertheless, we prove that the two theorems are true for central S-rings over any group, i.e., for S-rings that are contained in the center of the group ring of that group (such S-rings arise naturally in the supercharacter theory). Extending the concept of a B-group introduced by Wielandt, we show that every Camina group is a generalized B-group, whereas simple groups, with few exceptions, cannot be of this type.
38-49
Isomorphisms and Algorithmic Properties of Structures with Two Equivalences
Abstract
Isomorphisms and algorithmic properties of structures with two equivalences are considered using definability methods (developed by the author) for a graph in a bipartite graph and in a structure with two equivalences, which respect algorithmic and syntactic properties of the original structure.
50-57
Identifying Solutions to Systems of Equations in Semigroups with Finite Ideal
Abstract
A semigroup S is called an equational domain if any finite union of algebraic sets over S is again an algebraic set. We find necessary and sufficient conditions for a semigroup with a finite minimal two-sided ideal (in particular, a finite semigroup) to be an equational domain.
58-71
72-76
77-82
Sessions of the Seminar “Algebra i Logika”
83-85
Erratum
Erratum to: Linearly Minimal Jordan Algebras of Characteristic Other than 2
86-86