共查询到20条相似文献,搜索用时 0 毫秒
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2.
Alberto Facchini 《Annali di Matematica Pura ed Applicata》1981,128(1):359-374
Sunto Si dimostra che se M è un modulo Artiniano con zoccolo semplice su un anello commutativo R, allora EndR(M) è commutativo locale Noetheriano completo e che M, come EndR (M)-modulo, è l'inviluppo iniettivo dell'unico EndR(M)-modulo semplice. Si dimostra anche che ogni modulo di Loewy con invarianti di Loewy finiti è Artiniano e si siudia la successione degli invarianti di Loewy di un tale modulo. 相似文献
3.
D. J. Benson Wayne W. Wheeler 《Transactions of the American Mathematical Society》1999,351(9):3843-3855
Almost all of the basic theorems in the representation theory of finite groups have proofs that depend upon the Krull-Schmidt Theorem. Because this theorem holds only for finite-dimensional modules, however, the recent interest in infinitely generated modules raises the question of which results may hold more generally. In this paper we present an example showing that Green's Indecomposability Theorem fails for infinitely generated modules. By developing and applying some general properties of idempotent modules, we are also able to construct explicit examples of modules for which the cancellation property fails.
4.
Let (R, m) be a complete Noetherian local ring, I an ideal of R and M a nonzero Artinian R-module. In this paper it is shown that if p is a prime ideal of R such that dim R/p = 1 and (0:M p) is not finitely generated and for each i ? 2 the R-module Ext R i (M,R/p) is of finite length, then the R-module Ext R 1 (M, R/p) is not of finite length. Using this result, it is shown that for all finitely generated R-modules N with Supp(N) ? V (I) and for all integers i ? 0, the R-modules Ext R i (N,M) are of finite length, if and only if, for all finitely generated R-modules N with Supp(N) ? V (I) and for all integers i ? 0, the R-modules Ext R i (M,N) are of finite length. 相似文献
5.
A. V. Yakovlev 《Vestnik St. Petersburg University: Mathematics》2010,43(1):3-11
We consider a sufficiently large subcategory of the category of mixed abelian groups of finite torsion-free rank and its quotient catego ry obtained by annihilating those homomorphisms which factor through the torsion. We prove that the second category provides a good approximation to the first category, but is much simpler: the groups of morphisms in the second category are finite rank torsion-free groups. This renders it possible to exam ine direct decompositions of mixed groups by the same methods as in the case of finite rank torsion-free groups. 相似文献
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
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B. A. F. Wehrfritz 《Central European Journal of Mathematics》2007,5(4):686-695
Let G be a hypercyclic group. The most substantial results of this paper are the following. a) If G/G′ is 2-divisible, then G is 2-divisible. b) If G/G′ is a 2′-group, then G is a 2′-group. c) If G/G′ is divisible by finite-of-odd-order, then G/V is divisible by finite-of-odd-order, where V is the intersection of the lower central series (continued transfinitely) of O
2′ (G).
相似文献
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A. V. Yakovlev 《Journal of Mathematical Sciences》1990,52(3):3206-3216
It is proved that ifr
1
,r
2
, ...,r
s
;l
1
,l
2
, ...,l
t
are the ranks of the indecomposable summands of two direct decompositions of a torsion-free Abelian group of finite rank
and if s0 is the number of units among the numbers ri, while t0 is the number of units among the numbers lj, thenr
i
⩽n - t
0
,l
j
⩽n−s
0
for all i, j. Moreover, if for some i we have ri=n−t0, then among the lj's only one term is different from 1 and it is equal to n−t0; similarly if lj=n−s0 for some j. In addition, a construction is presented, allowing to form, from several indecomposable groups, a new group,
called a flower group, and it is proved that a flower group is indecomposable under natural restrictions on its defining parameters.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 160, pp. 272–285, 1987. 相似文献
12.
《Journal of Pure and Applied Algebra》2023,227(4):107260
We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. We also prove the same types of results in a generalized setting using a ring with linear topology. 相似文献
13.
Ikuo Nishitani 《Archiv der Mathematik》2006,87(3):206-210
We show that a finitely embedded module M over a commutative ring R is Artinian if the factor module M/(0 :M P) is finitely embedded for every prime ideal P of R.
Received: 10 June 2005 相似文献
14.
Jonas Sderberg 《Journal of Algebra》2004,280(2):610-623
In order to use dualization to study Hilbert functions of artinian level algebras we extend the notion of level sequences and cancellable sequences, introduced by Geramita and Lorenzini, to include Hilbert functions of certain artinian modules. As in the case of algebras a level sequence is cancellable, but now by dualization its reverse is also cancellable which gives a new condition on level sequences. We also give a characterization of the cancellable sequences involving Macaulay representations. 相似文献
15.
Muhammet Tamer Koşan 《Proceedings Mathematical Sciences》2009,119(4):453-458
Let R be a commutative Noetherian ring with non-zero identity and a be a maximal ideal of R. An R-module M is called minimax if there is a finitely generated submodule N of M such that M/N is Artinian. Over a Gorenstein local ring R of finite Krull dimension, we proved that the Socle of H
a
n
(R) is a minimax R-module for each n ≥ 0. 相似文献
16.
Patrick F. Smith 《Mathematische Zeitschrift》1975,144(3):283-288
17.
Takeshi Katsura 《Journal of Algebra》2008,319(9):3653-3665
We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a cyclic p-group is permutation projective. 相似文献
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R. Grigutis 《Lithuanian Mathematical Journal》1991,31(2):183-188
Vilnius University. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 2, pp. 275–281, April–June, 1991. 相似文献
20.
Jonas Söderberg 《Journal of Pure and Applied Algebra》2006,207(2):417-432
We prove that a sequence of positive integers (h0,h1,…,hc) is the Hilbert function of an artinian level module of embedding dimension two if and only if hi−1−2hi+hi+1≤0 for all 0≤i≤c, where we assume that h−1=hc+1=0. This generalizes a result already known for artinian level algebras. We provide two proofs, one using a deformation argument, the other a construction with monomial ideals. We also discuss liftings of artinian modules to modules of dimension one. 相似文献