共查询到20条相似文献,搜索用时 15 毫秒
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Liana M. ?ega 《Journal of Pure and Applied Algebra》2011,215(6):1263-1269
We prove that the Auslander-Reiten conjecture holds for commutative standard graded artinian algebras, in two situations: the first is under the assumption that the modules considered are graded and generated in a single degree. The second is under the assumption that the algebra is generic Gorenstein of socle degree 3. 相似文献
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Gerhard Behrendt 《Order》1993,10(1):65-75
A tower in an ordered set (X, ) is defined to be a subsetS ofX which has the property that for everysS there is a maximal chainC in {xX|xs} which is wholly contained inS. An ordered set (X, ) is called tower-homogeneous if every order isomorphism between towers in (X, ) can be extended to an automorphism of (X, ). It is shown that a finite ordered set is tower-homogeneous if and only if it can be built up from singletons stepwise by constructions of three different types. 相似文献
4.
Carl Faith 《代数通讯》2013,41(8):3983-3986
The aim of this paper is to give a new and direct proof of the theorem. 相似文献
5.
A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Such a polynomial is always a product of linear factors over K, although not every product of linear polynomials is a Wedderburn polynomial. In this paper, we establish various properties and characterizations of Wedderburn polynomials over K, and show that these polynomials form a complete modular lattice that is dual to the lattice of full algebraic subsets of K. Throughout the paper, we work in the general setting of an Ore skew polynomial ring K[t,S,D], where S is an endomorphism of K and D is an S-derivation on K. 相似文献
6.
Murray Marshall 《Mathematische Zeitschrift》2002,242(2):217-225
An extension of the Kadison-Dubois representation theorem is proved. This extends both the classical version [3] and the
preordering version given by Jacobi in [5]. It is then shown how this can be used to sharpen the results on representations
of strictly positive polynomials given by Jacobi and Prestel in [6].
Received: 10 January 2000; in final form: 20 September 2000 / Published online: 19 October 2001 相似文献
7.
We describe two complete partially ordered sets which are the intersection of complete linear orderings but which have no compatible Hausdorff topology. One is two-dimensional, while the second is countable, and leads to an example of a countable, compact, T
1 space with a countable base which is not the continuous image of any compact Hausdorff space. 相似文献
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Claus Michael Ringel 《Journal of Pure and Applied Algebra》2006,205(2):412-422
Let Λ be a commutative local uniserial ring with radical factor field k. We consider the category S(Λ) of embeddings of all possible submodules of finitely generated Λ-modules. In case Λ=Z/〈pn〉, where p is a prime, the problem of classifying the objects in S(Λ), up to isomorphism, has been posed by Garrett Birkhoff in 1934. In this paper we assume that Λ has Loewy length at least seven. We show that S(Λ) is controlled k-wild with a single control object I∈S(Λ). It follows that each finite dimensional k-algebra can be realized as a quotient End(X)/End(X)I of the endomorphism ring of some object X∈S(Λ) modulo the ideal End(X)I of all maps which factor through a finite direct sum of copies of I. 相似文献
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Let k be a field and let Λ be an indecomposable finite dimensional k-algebra such that there is a stable equivalence of Morita type between Λ and a self-injective split basic Nakayama algebra over k. We show that every indecomposable finitely generated Λ-module V has a universal deformation ring and we describe explicitly as a quotient ring of a power series ring over k in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to p-modular blocks of finite groups with cyclic defect groups. 相似文献
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Janko Marovt 《Linear algebra and its applications》2010,432(6):1595-1607
Let D be an arbitrary division ring and Mn(D) the multiplicative semigroup of all n×n matrices over D. We study non-degenerate, injective homomorphisms from M2(D) to M4(D). In particular, we present a structural result for the case when D is the ring of quaternions. 相似文献
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In this article we study the structure of highest weight modules for quantum groups defined over a commutative ring with particular emphasis on the structure theory for invariant bilinear forms on these modules. 相似文献
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Jeremy Haefner 《代数通讯》2013,41(2):445-481
We give necessary conditions for a map to be irreducible (in the category of finitely generated, torsion free modules) over a non-local, commutative ring and sufficient conditions when the ring is Bass. In particular, we show that an irreducible map of ZG, where G is a square free abelian group, must be a monomorphism with a simple cokernel. We also show that local endomorphism rings are necessary and sufficient for the existence of almost split sequences over a commutative Bass ring and we explicitly describe the modules and the maps in those sequences. The results in this paper enable us to describe the Auslander-Reiten quiver of a non-local Bass ring in [8]. 相似文献
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Giuseppe Baccella 《Journal of Algebra》2010,323(3):790-838
If R is a semiartinian von Neumann regular ring, then the set of primitive ideals of R, ordered by inclusion, is an artinian poset in which all maximal chains have a greatest element. Moreover, if has no infinite antichains, then the lattice of all ideals of R is anti-isomorphic to the lattice of all upper subsets of . Since the assignment defines a bijection from any set of representatives of simple right R-modules to , a natural partial order is induced in , under which the maximal elements are precisely those simple right R-modules which are finite dimensional over the respective endomorphism division rings; these are always R-injective. Given any artinian poset I with at least two elements and having a finite cofinal subset, a lower subset and a field D, we present a construction which produces a semiartinian and unit-regular D-algebra having the following features: (a) is order isomorphic to I; (b) the assignment realizes an anti-isomorphism from the lattice to the lattice of all upper subsets of ; (c) a non-maximal element of is injective if and only if it corresponds to an element of , thus is a right V-ring if and only if ; (d) is a right and left V-ring if and only if I is an antichain; (e) if I has finite dual Krull length, then is (right and left) hereditary; (f) if I is at most countable and , then is a countably dimensional D-algebra. 相似文献
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Marion Scheepers 《Order》1990,7(1):41-64
We introduce a partition relation which is an alternate for measuring how badly the ordinary partition relation fails, we develop its corresponding partition calculus and we determine its status for various typical partially ordered sets. 相似文献
17.
Let A be a commutative integral domain that is a finitely generated algebra over a field k of characteristic 0 and let ø be a k-algebra automorphism of A of finite order m. In this note we study the ring D(A;ø of differential operators introduced by A.D. Bell. We prove that if A is a free module over the fixed sub-ring A ø, with a basis containing 1, then D(A;ø) is isomorphic to the matrix ring Mm(D(A ø). It follows from Grothendieck's Generic Flatness Theorem that for an arbitrary A there is an element c?Asuch that D(A[c-1];ø)?M m(D(A[c-1]ø)). As an application, we consider the structure of D(A;ø)when A is a polynomial or Laurent polynomial ring over k and ø is a diagonalizable linear automorphism. 相似文献
18.
Gyula Lakos 《Linear algebra and its applications》2010,432(1):338-346
We generalize the Wiener-Hopf factorization of Laurent series to more general commutative coefficient rings, and we give explicit formulas for the decomposition. We emphasize the algebraic nature of this factorization. 相似文献
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The classical theorem of R. P. Dilworth asserts that a partially ordered set of width n can be partitioned into n chains. Dilworth's theorem plays a central role in the dimension theory of partially ordered sets since chain partitions can be used to provide embeddings of partially ordered sets in the Cartesian product of chains. In particular, the dimension of a partially-ordered set never exceeds its width. In this paper, we consider analogous problems in the setting of recursive combinatorics where it is required that the partially ordered set and any associated partition or embedding be described by recursive functions. We establish several theorems providing upper bounds on the recursive dimension of a partially ordered set in terms of its width. The proofs are highly combinatorial in nature and involve a detailed analysis of a 2-person game in which one person builds a partially ordered set one point at a time and the other builds the partition or embedding.This paper was prepared while the authors were supported, in part, by NSF grant ISP-80-11451. In addition, the second author received support under NSF grant MCS-80-01778 and the third author received support under NSF grant MCS-82-02172. 相似文献
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Frauke M. Bleher 《Advances in Mathematics》2010,225(3):1499-71
We determine the universal deformation rings R(G,V) of certain mod 2 representations V of a finite group G which belong to a 2-modular block of G whose defect groups are isomorphic to a generalized quaternion group D. We show that for these V, a question raised by the author and Chinburg concerning the relation of R(G,V) to D has an affirmative answer. We also show that R(G,V) is a complete intersection even though R(G/N,V) need not be for certain normal subgroups N of G which act trivially on V. 相似文献