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1.
E. A. Palyutin 《Algebra and Logic》2003,42(4):266-278
Our main goal is to prove that an infinite group is interpreted in every primitive connected non-superstable theory. Previously, we have introduced the concept of primitive connected theories, for which the quantifier elimination theorem was proved generalizing a similar elimination result for modules due to Baur, Monk, and Garavaglia. Here, we study primitive connected theories in which an infinite group is not interpreted, that is, theories that differ radically from theories of modules, but have a similar structure theory. Such are said to be antiadditive. (Note that theories of modules, as distinct from antiadditive ones, may be non-superstable.) 相似文献
2.
S. V. Limarenko 《Journal of Mathematical Sciences》2006,139(4):6723-6752
Some results concerning compressible modules, primitive rings, and weakly primitive rings are obtained. Properties of analogous
objects in the supercase are considered. The main result is the extended density theorem for superrings. In addition, rings
and modules graded by a group are studied.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 3, pp. 97–142, 2004. 相似文献
3.
We define and study universal Horn classes dual to varieties in both the syntactic and the semantic sense. Such classes, which
we call antivarieties, appear naturally, e.g., in graph theory and in formal language theory. The basic results are the characterization
theorem for antivarieties, the theorem on cores in axiomatizable color-families, and the decidability theorem for universal
theories of families of interpretations of formal languages.
Supported by RFFR grants Nos. 99-01-000485 and 96-01-00097, and also by DFG grant No. 436113/2670.
Translated fromAlgebra i Logika, Vol. 39, No. 1, pp. 3–22, January–February, 2000. 相似文献
4.
A. A. Stepanova 《Algebra and Logic》2006,45(3):172-179
We study into monoids S the class of all S-polygons over which is primitive normal, primitive connected, or additive, that
is, the monoids S the theory of any S-polygon over which is primitive normal, primitive connected, or additive. It is proved
that the class of all S-polygons is primitive normal iff S is a linearly ordered monoid, and that it is primitive connected
iff S is a group. It is pointed out that there exists no monoid S with an additive class of all S-polygons.
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Translated from Algebra i Logika, Vol. 45, No. 3, pp. 300–313, May–June, 2006. 相似文献
5.
6.
B. V. Petrenko 《Ukrainian Mathematical Journal》1997,49(2):281-288
In the theory of infinite groups, one of the most important useful generalizations of the classical Maschke theorem is the
Kovačs-Newman theorem, which establishes sufficient conditions for the existence of G-invariant complements in modules over a periodic group G finite over the center. We genralize the Kovačs-Newman theorem to the case of modules over a group ring KG, where K is a Dedekind domain.
Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 255–261,
February, 1997. 相似文献
7.
This paper contains two theorems concerning the theory of maximal Cohen–Macaulay modules. The first theorem proves that certain
Ext groups between maximal Cohen–Macaulay modules M and N must have finite length, provided only finitely many isomorphism classes of maximal Cohen–Macaulay modules exist having ranks
up to the sum of the ranks of M and N. This has several corollaries. In particular it proves that a Cohen–Macaulay lo cal ring of finite Cohen–Macaulay type has
an isolated singularity. A well-known theorem of Auslander gives the same conclusion but requires that the ring be Henselian.
Other corollaries of our result include statements concerning when a ring is Gorenstein or a complete intersection on the
punctured spectrum, and the recent theorem of Leuschke and Wiegand that the completion of an excellent Cohen–Macaulay local
ring of finite Cohen–Macaulay type is again of finite Cohen–Macaulay type . The second theorem proves that a complete local
Gorenstein domain of positive characteristic p and dimension d is F-rational if and only if the number of copies of R splitting out of divided by has a positive limit. This result relates to work of Smith and Van den Bergh. We call this limit the F-signature of the ring and give some of its properties.
Received: 6 May 2001 / Published online: 6 August 2002
Both authors were partially supported by the National Science Foundation. The second author was also partially supported by
the Clay Mathematics Institute. 相似文献
8.
A. A. Florinskii 《Journal of Mathematical Sciences》1999,97(4):4329-4335
Two theorems announced by the author are proved. The first theorem concerns the existence of connected metrizable extensions
of metric spaces. The second theorem is a slightly paradoxical assertion about the validity of the fixed-point principle.
Bibliography: 4 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 17, 1997, pp. 227–237. 相似文献
9.
In this paper, we mainly introduce the concept of weak relative [C, H]-Hopf modules and give the fundamental theorem of weak relative right [C, H]-Hopf modules.
Published in Russian in Matematicheskie Zametki, 2007, Vol. 82, No. 4, pp. 530–537.
The text was submitted by the authors in English. 相似文献
10.
A. N. Koryukin 《Algebra and Logic》1997,36(4):236-244
In [1], the question was posed as to whether or not all algebraic relations of skew derivations of prime rings follow from
primitive algebraic relations. Here we argue to obtain a negative answer to a milder question, and namely, an example is constructed
in which a pointed Hopf algebra H (generated as an algebra with unity by its relatively primitive elements) acts trivially
on the generalized centroid C of a prime ring R, but not all algebraic relations of skew derivations (corresponding to relatively
primitive elements in H) follow from primitive algebraic ones. The R in the counterexample is a free associative C-algebra.
Supported by ISF grant No. RPS300 and by RFFR grant No. 95-01-01356a.
Translated from Algebra i Logika, Vol. 36, No. 4, pp. 407–421, July–August, 1997. 相似文献
11.
S. V. Sudoplatov 《Algebra and Logic》2006,45(3):180-200
Previously, we obtained a syntactic characterization for the class of complete theories with finitely many pairwise non-isomorphic
countable models [1]. The most essential part of that characterization extends to Ehrenfeucht theories (i.e., those having
finitely many (but more than 1) pairwise non-isomorphic countable models). As the basic parameters defining a finite number
of countable models, Rudin-Keisler quasiorders are treated as well as distribution functions defining the number of limit
models for equivalence classes w.r.t. these quasiorders. Here, we argue to state that all possible parameters given in the
characterization theorem in [1] are realizable. Also, we describe Rudin-Keisler quasiorders in arbitrary small theories. The
construction of models of Ehrenfeucht theories with which we come up in the paper is based on using powerful digraphs which,
along with powerful types in Ehrenfeucht theories, always locally exist in saturated models of these theories.
Supported by RFBR grant Nos. 02-01-00258 and 05-01-00411.
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Translated from Algebra i Logika, Vol. 45, No. 3, pp. 314–353, May–June, 2006. 相似文献
12.
By using the Sierpiński continuum theorem, we prove that every upper-continuous two-valued mapping of a linearly connected
space (or even a c-connected space, i.e., a space in which any two points can be connected by a continuum) into the Sorgenfrey line is necessarily
constant.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1034–1039, August, 2007. 相似文献
13.
It is shown that polynilpotent groups with a single primitive defining relation have a decidable word problem.
Supported by RFBR grant No. 05-01-00292.
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Translated from Algebra i Logika, Vol. 45, No. 1, pp. 28–43, January–February, 2006. 相似文献
14.
V. I. Zenkov 《Algebra and Logic》1996,35(3):160-163
Using the basic theorem on the classification of finite simple groups, we answer one of the questions concerning the generation
of finite groups by the class of conjugate Abelian subgroups.
Supported by RFFR grant No. 93-01-01529.
Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 288–293, May–June, 1996. 相似文献
15.
I. A. Lavrov 《Algebra and Logic》1996,35(3):164-171
A new approach to the study of creative sets using the notion of a table is offered. Making use of tables conforming to recursively
enumerable sets, novel properties of creative sets are established. Harrington's theorem on the definability of creative sets
in the lattice of recursively enumerable sets is proved, and we reprove Lachlan's theorem which states that one of the factors
in a direct product of creative sets is again creative.
Supported by RFFR grant No. 93-01-16014.
Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 294–307, May–June, 1996. 相似文献
16.
We explain how to deduce the degenerate analogue of Ariki’s categorification theorem over the ground field
\mathbbC{\mathbb{C}} as an application of Schur–Weyl duality for higher levels and the Kazhdan–Lusztig conjecture in finite type A. We also discuss
some supplementary topics, including Young modules, tensoring with sign, tilting modules and Ringel duality. 相似文献
17.
We prove a structure theorem for the connected coassociative magmatic bialgebras. The space of primitive elements is an algebra
over an operad called the primitive operad. We prove that the primitive operad is magmatic generated by n−2 operations of arity n. The dimension of the space of all the n-ary operations of this primitive operad turns out to be the Fine number F
n−1. In short, the triple of operads (As, Mag, MagFine) is good.
The third author work is partially supported by FONDECYT Project 1060224 相似文献
18.
LetA
n, n≥0, be a variety of all Abelian groups whose exponental divides n. We establish a criterion of being primitive for varieties
of the formA
m
A
n, and study into the question of inducing primitive systems of elements in free groups of these. The results obtained give
a solution to the problem by Bachmuth and Mochizuki concerning the tame range of varietiesA
m
A
n for the case where m is freed of squares, and lend support to the conjecture by Bryant and Gupta as to inducing primitive,
systems for varieties likeA
pnA.
This author’s part is supported by RFFR grant No. 99-01-00567.
Translated fromAlgebra i Logika, Vol. 38, No. 5, pp. 513–530, September–October, 1999. 相似文献
19.
V. A. Artamonov 《Mathematical Notes》1996,59(4):356-360
We describe the structure of finitely generated modules over general quantum Laurent polynomials and prove that Artin modules
over general quantum Laurent polynomials are cyclic.
Translated fromMatematicheskie Zametki, Vol. 59, No. 4, pp. 497–503, April, 1996.
This research was partially supported by the Russian Foundation for the Basic Research under grant No. 93-011-1544 and by
the INTAS program under grant No. 93-2618. 相似文献
20.
V. A. Lyubetsky 《Algebra and Logic》1997,36(3):169-181
A set theory ZFI′ which does not employ the Law of the Excluded Middle φ ∀ ⊥ φ, for all φ, retians the stock of expressive
capacities of the classical set theory ZF, on the one hand, and has many of the features of an effective theory on the other.
In the article, a broad class of formulas σ is constructed for which ZF ⊥ σ implies ZFI′ ⊥ σ. This result provides a generalization
of Friedman's theorem on AE-arithmetic formulas. Besides, we prove transfer theorems of classical logic for the case of rings;
in particular, Hilbert's theorem on zeros and Artin's theorem on ordered fields are extended to the case of regular f-rings,
and we bring in appropriate upper bounds for them.
Supported by RFFR grant No. 93-012-1027.
Translated fromAlgebra i Logika, Vol. 36, No. 3, pp. 282–303, May–June, 1997. 相似文献