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Том 56, № 5 (2017)
- Год: 2017
- Статей: 8
- URL: https://journal-vniispk.ru/0002-5232/issue/view/14545
Article
A Representation of Virtual Braids by Automorphisms
Аннотация
We study a representation of the virtual braid group VBn into the automorphism group of a free product of a free group and a free Abelian group, proposed by S. Kamada. It is proved that the given representation is equivalent to the representation constructed in [http://arxiv.org/abs/1603.01425]; i.e. the kernels of these representations coincide.
355-361
The Specht Property of L-Varieties of Vector Spaces
Аннотация
Conditions are explored which imply the finite basis property for identities of vector spaces embedded in associative algebras over an infinite field. An L-variety having no finite basis of identities, which is the join of two Spechtian L-varieties, is exemplified.
362-369
Strong Decidability and Strong Recognizability
Аннотация
Extensions of Johansson’s minimal logic J are considered. It is proved that families of negative and nontrivial logics and a series of other families are strongly decidable over J. This means that, given any finite list Rul of axiom schemes and rules of inference, we can effectively verify whether the logic with axioms and schemes, J + Rul, belongs to a given family. Strong recognizability over J is proved for known logics Neg, Gl, and KC as well as for logics LC and NC and all their extensions.
370-385
Hyperidentities of Quasilinear Clones Containing Creative Functions
Аннотация
We consider the possibility for separating by hyperidentities clones of quasilinear functions defined on the set {0, 1, 2} with values in the set {0, 1}. It is proved that every creative clone of this kind can be separated by a hyperidentity from any noncreative clone comparable with it.
386-394
Divisible Rigid Groups. Algebraic Closedness and Elementary Theory
Аннотация
A group G is said to be rigid if it contains a normal series G = G1 > G2 > … > Gm > Gm+1 = 1, whose quotients Gi/Gi+1 are Abelian and, treated as right ℤ[G/Gi]-modules, are torsion-free. A rigid group G is divisible if elements of the quotient Gi/Gi+1 are divisible by nonzero elements of the ring ℤ[G/Gi]. Every rigid group is embedded in a divisible one. We prove two theorems. Theorem 1 says that the following three conditions for a group G are equivalent: G is algebraically closed in the class Σm of all m-rigid groups; G is existentially closed in the class Σm; G is a divisible m-rigid group. Theorem 2 states that the elementary theory of a class of divisible m-rigid groups is complete.
395-408
Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries
Аннотация
We give a characterization of complete strongly dually atomic lattices having unique irredundant decompositions which are also canonical. It is shown that all known characterizations of lattices with unique irredundant decompositions are a consequence of this result. In addition, upper continuous closure lattices of convex geometries with (unique) irredundant decompositions are characterized.
409-424
Molien–Wedderburn Theorem for Associative Conformal Algebras with Finite Faithful Representation
427-428
Communications
A Computable Structure with Nonstandard Computability
425-426