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Том 57, № 2 (2018)
- Год: 2018
- Статей: 8
- URL: https://journals.rcsi.science/0002-5232/issue/view/14548
Article
The Tensor Completion Functor in Categories of Exponential MR-Groups
Аннотация
The notion of an exponential R-group, where R is an arbitrary associative ring with unity, was introduced by R. Lyndon. A. G. Myasnikov and V. N. Remeslennikov refined this notion by adding an extra axiom. In particular, the new notion of an exponential MR-group is an immediate generalization of the notion of an R-module to the case of noncommutative groups. Basic concepts in the theory of exponential MR-groups are presented, and we propose a particular method for constructing tensor completion—the key construction in the category of MR-groups. As a consequence, free MR-groups and free MR-products are described using the language of group constructions.
89-97
Degrees of Autostability for Prime Boolean Algebras
Аннотация
We look at the concept of algorithmic complexity of isomorphisms between computable copies of Boolean algebras. Degrees of autostability are found for all prime Boolean algebras. It is shown that for any ordinals α and β with the condition 0 ≤ α ≤ β ≤ ω, there is a decidable model for which 0(α) is a degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability. It is proved that for any nonzero ordinal β ≤ ω, there is a decidable model for which there is no degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability.
98-114
Finite Almost Simple Groups Whose Gruenberg–Kegel Graphs Coincide with Gruenberg–Kegel Graphs of Solvable Groups
Аннотация
It is shown that the Gruenberg–Kegel graph of a finite almost simple group is equal to the Gruenberg–Kegel graph of some finite solvable group iff it does not contain 3-cocliques. Furthermore, we obtain a description of finite almost simple groups whose Gruenberg–Kegel graphs contain no 3-cocliques.
115-129
130-140
Edge-Symmetric Distance-Regular Coverings of Complete Graphs: the Almost Simple Case
Аннотация
We complete the classification of edge-symmetric distance-regular coverings of complete graphs with r /∉ {2, k, (k − 1)/μ} for the case of the almost simple action of an automorphism group of a graph on a set of its antipodal classes; here r is the order of an antipodal class.
141-152
153-160
Sessions of the Seminar “Algebra i Logika”
166-168
Communications
Jump Inversions of Algebraic Structures and the Σ-Definability
161-165