We investigate the semirings over which all simple semimodules are injective. In ring and module theory, the rings with an analogous condition are called V-rings. Therefore it is natural to call the semirings under ...
Under study is the category A of the possibly noncommutative H-module algebras that are mapped homomorphically onto commutative algebras. The H-equivariant Martindale ring of quotients Q H(A) is shown to be a finite-dimensional ...
Consider a von Neumann algebra M with a faithful normal semifinite trace τ. We prove that each order bounded sequence of τ-compact operators includes a subsequence whose arithmetic averages converge in τ. We also prove a ...
We find new necessary and sufficient conditions for the commutativity of projections in terms of operator inequalities. We apply these inequalities to characterize a trace on von Neumann algebras in the class of all positive ...
If ν and μ are some Δcomputable numberings of families of sets of the naturals then P(x,y) ⇔ ν(x)′ ≠ μ(y) is a Σpredicate. Deriving corollaries from this result, we obtain a sufficient condition for existence of a Δcomputable ...
We consider the class of so-called k-quasidiscrete linear orderings, show that every k-quasi-discrete ordering of low degree has a computable representation, and study estimates for the complexity of all isomorphisms ...
We construct the classes of functions analytic in the unit disk, other than lacunary, and possessing the following property: If a function belongs to one of these classes and the sum of the squares of its coefficients is ...
We show that the class of varieties of multioperator superalgebras, defined by multilinear identities and considered up to rational equivalence, coincides with the class of varieties of superalgebras over an operad. We ...
Given a countable algebraic structure B with no degree we find sufficient conditions for the existence of a countable structure A with the following properties: (1) for every isomorphic copy of A there is an isomorphic ...
Given an arbitrary quasiprojective right R-module P, we prove that every module in the category σ(P) is weakly regular if and only if every module in σ(M/I(M)) is lifting, where M is a generating object in σ(P). In particular, ...
We obtain a solution to the Hilbert boundary value problem in the theory of analytic functions on the half-plane in the case that the coefficients of the boundary condition have countably many discontinuity points of the ...
We obtain some estimates for the distortions of the moduli of quadrilaterals, the reduced moduli, and Robin capacities depending on the variation of the boundary of a domain. We show that for sufficiently smooth variations ...
We give a direct proof of the fact that every variety of many-sorted universal algebras is rationally equivalent to a variety of algebras over some FSet-multicategory (a many-sorted analog of FSet-operads). The construction ...
Under study are some conditions for the weakly regular modules to be closed under direct sums and the rings over which all modules are weakly regular. For an arbitrary right R-module M, we prove that every module in the ...
We consider the Fuchsian groups of linear-fractional transformations. We propose a new method for presenting automorphic forms as gap series over an appropriate subset of transformations of the group which is not a subgroup. ...
We show that varieties of algebras over abstract clones and over the corresponding operads are rationally equivalent. We introduce the class of operads (which we call commutative for definiteness) such that the varieties ...