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1.
S. N. Chernikov 《Mathematical Notes》1968,4(1):543-545
It is proved that if a periodic group
has an extremal normal divisor
, determining a complete abelian factor group
, then the center of the group
contains a complete abelian subgroup
, satisfying the relation
and intersecting
on a finite subgroup. It is also established with the aid of this proposition that every periodic group of automorphisms of an extremal group
is a finite extension of a contained in it subgroup of inner automorphisms of the group
.Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 91–96, July, 1968. 相似文献
2.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
3.
D. N. Dudin 《Mathematical Notes》1968,3(1):42-44
For an algebra
of subsets of a set X there is constructed a set
and an algebra of its subsets so that the mapping
is a one-to-one correspondence between
and
and for each additive measure on
the measure
on
defined by the equation
is countably additive.Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 71–76, January, 1968.The author wishes to express his deep appreciation to S. V. Fomin, under whose guidance this paper was written. 相似文献
4.
A. Ya. Khelemskii 《Mathematical Notes》1977,21(1):51-54
Let
and
be algebras of local and quasilocal observable spin systems corresponding to the group Zr,
be a differentiation invariant with respect to displacements. The question of representation of D in the form of formal Hamiltonian
formed by the displacements of an elementx ε
is considered. It is shown that such a representation exists if the condition
holds, where
means an element obtained from the elements [TkX,a] by some r-multiple process of summation.
Translated from Matematicheskii Zametki, Vol. 21, No. 1, pp. 93–98, January, 1977. 相似文献
5.
Let K be a field and
a non-trivial valuation ring of K withm as its maximal ideal. Denote by
and
the rings of polynomials f∈K[X] and rational functions f∈K(X) resp. such that
. We prove that for one variable X we have
if and only if the completion of (K,
) is locally compact or algebraically closed. In the second case—i.e. if K is dense in the algebraic closure of (K,
)—we even get
for any number of variables X=(X1,...,Xn).
This work contains parts of the second author's thesis [Ri] written under the supervision of the first author. 相似文献
6.
M. I. Anokhin 《Mathematical Notes》1997,61(1):3-8
LetF be a free group with at most countable system
of free generators, letR be its normal subgroup recursively enumerable with respect to
, and let
be a variety of groups that differs from
and for which the corresponding verbal subgroupV of the free group of countable rank is recursive. It is proved that the word problem inF/V(R) is solvable if and only if this problem is solvable inF/R, and if
, then there exists anR such, that the conjugacy problem inF/R is solvable, but this problem is unsolvable inF/V(R) for any Abelian variety
(all algorithmic problems are regarded with respect to the images of
under the corresponding natural epimorphisms).
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 3–9, January, 1997.
Translated by M. I. Anokhin 相似文献
7.
V. Yu. Popov 《Mathematical Notes》2000,67(4):495-504
An example of a series of varieties of rings
with the finite basis property is constructed for which the word problem in the relatively free ring
of rankn in the variety
is decidable if and only ifn <p.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 582–594, April, 2000. 相似文献
8.
Götz Brunner 《Israel Journal of Mathematics》1972,12(3):306-313
In the definition ofCW-complexes, the one-point spaceP, respectively the spaceP∪* with basepoint *, play the roll of the only “building-stone”. Let
be a family of compact spaces. Then the definition of a generalizedCW-complex over
is obtained from the definition of aCW-complex by replacingP by the spaces of
and formation of the mapping cone by a slightly modified construction. LetCW
* denote the category of all pointed spaces which have the homotopy type of a generalizedCW-complex over
. If
, thenCW
* is the category of all pointedCW-spaces.CW
* is closed under the formation of direct sums and of mapping cones, cylinders and tori, and is formally characterized as
the smallest such subcategory of Top * containing the spaces W∪*,
. Following the methods of E. H. Brown, it is proved, that any half exact homotopy functor onCW
* is representable, and any cohomology theory onCW
is naturally equivalent to the cohomology theory of an Ω-spectrum; for example, the singular cohomo logy is representable
onCW
for any family
of compact spaces.
相似文献
9.
E. I. Timoshenko 《Algebra and Logic》1998,37(6):391-398
Part of any basis of a relatively free group
in the variety
is called a primitive system of elements. We provide a criterion of being primitive for
, where
is a variety of Abelian groups satisfying xm=1, and
a variety generated by a finite group. Let
be a variety of nilpotent groups of class ≤c. It is proved that, for the group
, the property of being primitive for an element g is stronger than the condition of being unimodular on a vector composed
of values of Fox derivatives in the ring
. The group
is not residually finite whenever a system of elements is primitive.
Supported by RFFR grant No. 96-01-01948.
Translated fromAlgebra i Logika, Vol. 37, No. 6, pp. 687–699, November–December, 1998. 相似文献
10.
The classical factorization method reduces the study of a system of ordinary differential equations Ut=[U+, U] to solving algebraic equations. Here U(t) belongs to a Lie algebra
which is the direct sum of its subalgebras
and
, where “+” signifies the projection on
. We generalize this method to the case
. The corresponding quadratic systems are reducible to a linear system with variable coefficients. It is shown that the generalized
version of the factorization method can also be applied to Liouville equation-type systems of partial differential equations.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 3, pp. 339–350, March, 1997. 相似文献
11.
L. A. Skornyakov 《Mathematical Notes》1972,11(4):281-285
We describe varieties
of semigroups such that every retract of a semigroup which is free in
is either one-element or free in
.Translated from Matematicheskie Zametki, Vol. 11, No. 4, pp. 463–470, April, 1972. 相似文献
12.
Karl-Hermann Neeb 《Semigroup Forum》1996,53(1):230-261
We say that an invariant convex coneW in a Lie algebras
is elliptic if its interior consists of elliptic elements of
. If such a cone exists, then
has a compactly embedded Cartan subalgebra. The first main result, of this paper is a characterization of those Lie algebras,
which contain elliptic invariant cones. If
is an invariant domain in such a cone, then we characterize the invariant locally convex functions onD by their restrictions to
where
is a compactly embedded Cartan subalgebra. 相似文献
13.
T. Levasseur 《Transformation Groups》1998,3(4):337-353
Let
u
be a compact Lie algebra and let
u
be its complexification. Let ζ−1/2 be the inverse on the set of regular elements of
u
of a square root of the discriminant of
. Generalizing a result of W. Lichtenstein in the case
u
=
(n, ℂ) or
(nℝ), we prove that ∂(q).ζ1/2 is non zero for all harmonic polynomialsq ∈S(
) \ {0}. This fact is deduced from results about equivariantD-modules supported on the nilpotent cone of
. 相似文献
14.
In this paper, we suggest a new functional approach to the study of group classes which enables us to describe all formations and Fitting classes of finite groups in the language of functions. The notions of
-fibered formation and of
-fibered Fitting class with direction are introduced. A direction is defined as a mapping of the set
of all primes into the set of all nonempty Fitting formations. The existence of infinitely many mappings of this kind makes it possible to construct new forms of formations and Fitting classes for a given nonempty set
. In particular, an
-local formation is an
-fibered formation with a direction such that
for any prime p. In the paper we study some basic properties of
-fibered formations and of
-fibered Fitting classes with direction and obtain the structure of their minimal satellites for a given . 相似文献
15.
This paper examines the following question. If
and
are saturated formations then
is defined to be the class of all soluble groups whose
belong to
. In general
is a formation, but need not be a saturated formation. Here the smallest saturated formation containing
is studied. 相似文献
16.
L. I. Danilov 《Mathematical Notes》1997,61(1):48-57
We consider Stepanov almost periodic functions μ ∈
ranging in the metric space
of Borel probability measures on a complete separable metric space
is equipped with the Prokhorov metric). The main result is as follows: a function
, belongs to
if and only if for each bounded continuous function
, the function
is Stepanov almost periodic (of order 1) and
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 57–68, January, 1997.
Translated by I. P. Zvyagin 相似文献
17.
For any partial groupoid
, let Fr
be the free extension of
to a total groupoid. We show that
implies
and that the theory of Fr
is uniformly recursive in the theory of
. These results fail if “groupoid” is replaced by “semigroup”, “commutative semigroup”, “group”, “abelian group”, “semilattice”,
“K-lattice” for any nontrivial varietyK of lattices, or “Boolean algebra”.
Research supported in part by NSF Grant MCS78-01867. We thank the referee for his valuable comments.
Presented by B. Jónsson. 相似文献
18.
Günter Mayer 《Numerische Mathematik》1985,46(1):69-83
Summary Let
be a real irreduciblen×n interval matrix. Then a necessary and sufficient condition is given for the sequence
of the powers of an interval matrix
to converge to a matrix
which is not the null matrix. In addition a criterion for
is proved to decide whether the limit matrix
satisfies the condition of symmetry
. 相似文献
19.
Andreas Blass 《Archive for Mathematical Logic》1990,30(1):1-11
We prove several theorems about the cardinal
associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps from to, all families of size
are below all unbounded families. With respect to a natural ordering of filters on, all filters generated by
sets are below all non-feeble filters. If
then
and
. (The definitions of these cardinals are recalled in the introduction.) Finally, some consequences deduced from
by Laflamme are shown to be equivalent to
. 相似文献
20.
M. B. Zvyagina 《Journal of Mathematical Sciences》1998,89(2):1122-1126
Let Λ be an associative ring with identity and let
be the category of left unitary Λ-modules. A subcateqory
of the category
is said to be small if the pairwise nonisomorphic objects of
form a set. The main result of this paper consists of the fact that for every small full subcategory
, there exists a ring Γ such that
is dual to a small full subcategory of the category
. Some applications of this result are indicated. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 66–73. 相似文献