共查询到20条相似文献,搜索用时 437 毫秒
1.
We study injective hulls of simple modules over differential operator rings R[θ; d], providing necessary conditions under which these modules are locally Artinian. As a consequence, we characterize Ore extensions of S = K[x][θ; σ, d] for σ a K-linear automorphism and d a K-linear σ-derivation of K[x] such that injective hulls of simple S-modules are locally Artinian. 相似文献
2.
《代数通讯》2013,41(12):5335-5343
In this paper, we define the power stably free dimension for rings. Using its relations with other dimensions, we get a classification of rings. Moreover, we give the equivalent characterizations of a ring with power stably free dimension 0, 1 respectively. For a commutative ring R in which each f. g. module has a finite power stably free dimension, we show that R[x 1, …, xn ] is connected and all f. g. projective modules over R[x 1, …, xn ] are power free. 相似文献
3.
Gabriele Steidl 《Mathematische Nachrichten》1990,145(1):151-168
This paper is devoted to the introduction of extension rings S : = R[x]/gR[x] with a suitable polynomial g ? R[x] of arbitrary commutative rings R with identity and to the development of a normal basis concept of S over R, which is similar to that of Galois extensions of finite fields. We prove new results for Galois extensions of local rings and apply them together with the Chinese remainder theorem to solve the above task in a constructive way. 相似文献
4.
ABSTRACT In this paper, we study the behavior of the couniform (or dual Goldie) dimension of a module under various polynomial extensions. For a ring automorphism σ ∈ Aut(R), we use the notion of a σ-compatible module M R to obtain results on the couniform dimension of the polynomial modules M[x], M[x ?1], and M[x, x ?1] over suitable skew extension rings. 相似文献
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Warren Wm. McGovern 《Acta Mathematica Hungarica》2004,105(3):215-230
We study two rings of quotients of C(X), the ring of continuous functions on the Tychonoff space X. The first, F(X), is the ring of quotients induced by the filter of ideals consisting of dense finite intersections of fixed maximal ideals.
The second, C[F], is the ring of quotients induced by the filter of dense cofinite subspaces of X. After some preliminary information we explicitly describe in §2 and §3 the constructions of these rings of quotients. In
the third section, we use F(X)and C[F] to define and study the class of h-points and h-spaces. In particular, we show that C-spaces and P-spaces are h-spaces. In the last section we construct an ideal of C(X)which will be used to give an ideal theoretic characterization of h-points.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
In this article, we define a new associative dialgebra over a polynomial algebra F[x, y] with two indeterminates x and y. Left derivations, right derivations, derivations, and automorphisms of F[x, y] as associative dialgebra are determined. Meanwhile, we also determine all homogeneous derivations of F[x, y] as ?-graded Leibniz algebra, and automorphisms of Leibniz algebra F[x, y] preserving the standard filtration. 相似文献
10.
Suppose that in every finite even order subgroup F of a periodic group G, the equality [u, x]2 = 1 holds for any involution u of F and for an arbitrary element x of F. Then the subgroup I generated by all involutions in G is locally finite and is a 2-group. In addition, the normal closure of every subgroup of order 2 in G is commutative. 相似文献
11.
G. A. Garkusha 《Journal of Mathematical Sciences》2002,112(3):4303-4312
The classes of FP-injective and weakly quasi-Frobenius rings are investigated. The properties of both classes of rings are closely related to the embedding of finitely presented modules in fp-flat and free modules, respectively. Using these properties, we characterize the classes of coherent CF- and FGF-rings. Moreover, it is proved that the group ring R(G) is FP-injective (weakly quasi-Frobenius, respectively) if and only if the ring R is FP-injective (weakly quasi-Frobenius) and G is locally finite. Bibliography: 15 titles. 相似文献
12.
A. D. S. Goncalves J. F. C. Machado G N. De Oliveira 《Linear and Multilinear Algebra》2013,61(3-4):227-234
Let V be a finite dimensional vector space over the field Fand φ (x)?F[x].Letx V → V be a linear operator. Let Sφ be the set consisting of the vectors whose minimal polynomial φ(x)together with the zero vector We give necessary and sufficieni condition for S φ to be a subspace. 相似文献
13.
《代数通讯》2013,41(3):1219-1227
Abstract A radical γ has the Amitsur property, if γ(A[x]) = (γ(A[x]) ∩ A)[x] for every ring A. To any radical γ with Amitsur property we construct the smallest radical γ x which coincides with γ on polynomial rings. Distinct special radicals with Amitsur property are given which coincide on simple rings and on polynomial rings, answering thus a stronger version of M. Ferrero's problem. Radicals γ with Amitsur property are characterized which satisfy A[x, y] ∈ γ whenever A[x] ∈ γ. 相似文献
14.
Every module over an Iwanaga–Gorenstein ring has a Gorenstein flat cover [13] (however, only a few nontrivial examples are
known). Integral group rings over polycyclic-by-finite groups are Iwanaga–Gorenstein [10] and so their modules have such covers.
In particular, modules over integral group rings of finite groups have these covers. In this article we initiate a study of
these covers over these group rings. To do so we study the so-called Gorenstein cotorsion modules, i.e. the modules that split
under Gorenstein flat modules. When the ring is ℤ, these are just the usual cotorsion modules. Harrison [16] gave a complete
characterization of torsion free cotorsion ℤ-modules. We show that with appropriate modifications Harrison's results carry
over to integral group rings ℤG when G is finite. So we classify the Gorenstein cotorsion modules which are also Gorenstein flat over these ℤG. Using these results we classify modules that can be the kernels of Gorenstein flat covers of integral group rings of finite
groups. In so doing we necessarily give examples of such covers. We use the tools we develop to associate an integer invariant
n with every finite group G and prime p. We show 1≤n≤|G : P| where P is a Sylow p-subgroup of G and gives some indication of the significance of this invariant. We also use the results of the paper to describe the co-Galois
groups associated to the Gorenstein flat cover of a ℤG-module.
Presented by A. Verschoren
Mathematics Subject Classifications (2000) 20C05, 16E65. 相似文献
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《代数通讯》2013,41(8):2563-2568
Given a scheme X, we show that the automorphism functor of a quasi-coherent @x-module of finite presentation F is representable if and only if F is locally free. The main technical tool of independent interest is a fibre wise criterion for flatness, which works without any assumptions about the base. 相似文献
17.
A. Nikseresht 《代数通讯》2013,41(1):292-311
In two articles, Anderson and Valdes-Leon generalized the theory of factorization in integral domains to commutative rings with zero divisors and to modules. Here we investigate some factorization properties in modules and state a result that relates factorization properties of an R-module, M, to the factorization properties of M as an (R/Ann(M))-module. Furthermore, we will investigate when a polynomial module, M[x], has the bounded factorization property, assuming that M has this property. 相似文献
18.
A. A. Gerko 《Journal of Mathematical Sciences》2007,142(4):2205-2232
For finite modules over a local ring and complexes with finitely generated homology, we consider several homological invariants
sharing some basic properties with projective dimension.
In the second section, we introduce the notion of a semidualizing complex, which is a generalization of both a dualizing complex and a suitable module. Our goal is to establish some common properties of such complexes and the homological dimension with respect to them.
Basic properties are investigated in Sec. 2.1. In Sec. 2.2, we study the structure of the set of semidualizing complexes over
a local ring, which is closely related to the conjecture of Avramov-Foxby on the transitivity of the G-dimension. In particular,
we prove that, for a pair of semidualizing complexes X
1 and X
2 such that G
X2, we have X
2 ≃ X
1 ⊗
R
L
RHom
R
(X
1, X
2). Specializing to the case of semidualizing modules over Artinian rings, we obtain a number of quantitative results for the
rings possessing a configuration of semidualizing modules of special form. For the rings with m
3=0, this condition reduces to the existence of a nontrivial semidualizing module, and we prove a number of structural results
in this case.
In the third section, we consider the class of modules that contains the modules of finite CI-dimension and enjoys some nice
additional properties, in particular, good behavior in short exact sequences.
In the fourth section, we introduce a new homological invariant, CM-dimension, which provides a characterization for Cohen-Macaulay
rings in precisely the same way as projective dimension does for regular rings, CI-dimension for locally complete intersections,
and G-dimension for Gorenstein rings.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 30, Algebra,
2005. 相似文献
19.
Ebrahim Hashemi 《Mediterranean Journal of Mathematics》2011,8(2):207-214
Let R be a ring with unity and M be a right R-module. The system M[x] forms a left near R[x]-module under addition and substitution operations. In this paper we extend the study of annihilator conditions on nearring
of polynomials to left near R[x]-module M[x], when M is a reduced Baer module. Also, we give a characterization of reduced modules. As a corollary we obtain some results of Birkenmeier
and Huang [3]. 相似文献
20.
Let R be any ring. A right R-module M is called n-copure projective if Ext1(M, N) = 0 for any right R-module N with fd(N) ≤ n, and M is said to be strongly copure projective if Ext i (M, F) = 0 for all flat right R-modules F and all i ≥ 1. In this article, firstly, we present some general properties of n-copure projective modules and strongly copure projective modules. Then we define and investigate copure projective dimensions of modules and rings. Finally, more properties and applications of n-copure projective modules, strongly copure projective modules and copure projective dimensions are given over coherent rings with finite self-FP-injective dimension. 相似文献