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1.
Let R be a ring and P be an (infinite dimensional) partial tilting module. We show that the perpendicular category of P is equivalent to the full module category where and ?R is the Bongartz complement of P modulo its P-trace. Moreover, there is a ring epimorphism φ:R→S. We characterize the case when φ is a perfect localization. By [Riccardo Colpi, Alberto Tonolo, Jan Trlifaj, Partial cotilting modules and the lattices induced by them, Comm. Algebra 25 (10) (1997) 3225-3237], there exist mutually inverse isomorphisms μ′ and ν′ between the interval in the lattice of torsion classes in , and the lattice of all torsion classes in . We provide necessary and sufficient conditions for μ′ and ν′ to preserve tilting torsion classes. As a consequence, we show that these conditions are always satisfied when R is a Dedekind domain, and if P is finitely presented and R is an artin algebra, then the conditions reduce to the trivial ones, namely that each value of μ′ and ν′ contains all injectives. 相似文献
2.
We will prove that if a ring R is either countable or a Prüfer domain, then n-cotilting R-modules are pure injective. We can apply and modify a very nice argument due to Jensen and Lenzing [14] showing that algebraic compactness follows from splitting of canonical direct sums in cartesian products.Received: 3 February 2004 相似文献
3.
Ryo Takahashi 《Advances in Mathematics》2010,225(4):2076-399
Various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics. In this paper, as a higher-dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a finite p-group due to Benson, Carlson and Rickard, we consider classifying thick subcategories of the stable category of Cohen-Macaulay modules over a Gorenstein local ring. The main result of this paper yields a complete classification of the thick subcategories of the stable category of Cohen-Macaulay modules over a local hypersurface in terms of specialization-closed subsets of the prime ideal spectrum of the ring which are contained in its singular locus. 相似文献
4.
We introduce a notion of Gorenstein R-algebras over a commutative Gorenstein ring R. Then we provide a necessary and sufficient condition for a tilting complex over a Gorenstein R-algebra A to have a Gorenstein R-algebra B as the endomorphism algebra and a construction of such a tilting complex. Furthermore, we provide an example of a tilting complex over a Gorenstein R-algebra A whose endomorphism algebra is not a Gorenstein R-algebra. 相似文献
5.
Robin Houston 《Journal of Pure and Applied Algebra》2008,212(2):394-400
If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive. 相似文献
6.
Meral Arnavut 《Journal of Pure and Applied Algebra》2007,208(2):739-760
In this article we consider finitely generated torsion-free modules over certain one-dimensional commutative Noetherian rings R. We assume there exists a positive integer NR such that, for every indecomposable R-module M and for every minimal prime ideal P of R, the dimension of MP, as a vector space over the field RP, is less than or equal to NR. If a nonzero indecomposable R-module M is such that all the localizations MP as vector spaces over the fields RP have the same dimension r, for every minimal prime P of R, then r=1,2,3,4 or 6. Let n be an integer ≥8. We show that if M is an R-module such that the vector space dimensions of the MP are between n and 2n−8, then M decomposes non-trivially. For each n≥8, we exhibit a semilocal ring and an indecomposable module for which the relevant dimensions range from n to 2n−7. These results require a mild equicharacteristic assumption; we also discuss bounds in the non-equicharacteristic case. 相似文献
7.
Dario Spirito 《Journal of Pure and Applied Algebra》2019,223(3):1322-1336
We study the set of localizations of an integral domain from a topological point of view, showing that it is always a spectral space and characterizing when it is a proconstructible subspace of the space of all overrings. We then study the same problems in the case of quotient rings, flat overrings and sublocalizations. 相似文献
8.
A module M is called product closed if every hereditary pretorsion class in σ[M] is closed under products in σ[M]. Every module M which is locally of finite length (every finitely generated submodule of M has finite length) is product closed and every product closed module M is semilocal (M/J(M) is semisimple). Let be product closed and projective in σ[M]. It is shown that (1) M is semiartinian; (2) if M is finitely generated then M satisfies the DCC on fully invariant submodules; (3) M has finite length if M is finitely generated and every hereditary pretorsion class in σ[M] is M-dominated. If the ring R is commutative it is proven that M is product closed if and only if M is locally of finite length. 相似文献
9.
Let R be a commutative noetherian henselian non-Gorenstein local ring of depth zero. Denote by modR the category of all finitely generated R-modules, and by the full subcategory of modR consisting of all R-modules of Gorenstein dimension zero. We prove in this paper that if contains a non-free module, then it is not precovering in modR, in particular, there exist infinitely many isomorphism classes of indecomposable R-modules of Gorenstein dimension zero. 相似文献
10.
Pooyan Moradifar Shahab Rajabi Siamak Yassemi 《Journal of Pure and Applied Algebra》2018,222(11):3757-3773
Given a non-unit, non-zero-divisor, central element x of a ring Λ, it is well known that many properties or invariants of Λ determine, and are determined by, those of and . In the present paper, we investigate how the property of “being tilting” behaves in this situation. It turns out that any tilting module over Λ gives rise to tilting modules over and after localization and passing to quotient respectively. On the other hand, it is proved that under some mild conditions, a module over Λ is tilting if its corresponding localization and quotient are tilting over and respectively. 相似文献
11.
The present paper is a sequel to our previous work on almost uniserial rings and modules, which appeared in the Journal of Algebra in 2016; it studies rings over which every (left and right) module is almost serial. A module is almost uniserial if any two of its submodules are either comparable in inclusion or isomorphic. And a module is almost serial if it is a direct sum of almost uniserial modules. The results of the paper are inspired by a characterization of Artinian serial rings as rings having all left (or right) modules serial. We prove that if R is a local ring and all left R-modules are almost serial then R is an Artinian ring which is uniserial either on the left or on the right. We also produce a connection between local rings having all left and right modules almost serial, local balanced rings studied by Dlab and Ringel and local Köthe rings. Finally we prove Morita invariance of the almost serial property and list some consequences. 相似文献
12.
Adeleh Abdolghafourian Mohammad A. Iranmanesh Alice C. Niemeyer 《Journal of Pure and Applied Algebra》2017,221(10):2482-2493
The Divisibility Graph of a finite group G has vertex set the set of conjugacy class sizes of non-central elements in G and two vertices are connected by an edge if one divides the other. We determine the connected components of the Divisibility Graph of the finite groups of Lie type in odd characteristic. 相似文献
13.
14.
Mitsuo Hoshino 《Journal of Pure and Applied Algebra》2003,177(2):159-175
Let A be an artin algebra and e∈A an idempotent with add(eAA)=add(D(AAe)). Then a projective resolution of AeeAe gives rise to tilting complexes for A, where P(l)• is of term length l+1. In particular, if A is self-injective, then is self-injective and has the same Nakayama permutation as A. In case A is a finite dimensional algebra over a field and eAe is a Nakayama algebra, a projective resolution of eAe over the enveloping algebra of eAe gives rise to two-sided tilting complexes {T(2l)•}l?1 for A, where T(2l)• is of term length 2l+1. In particular, if eAe is of Loewy length two, then we get tilting complexes {T(l)•}l?1 for A, where T(l)• is of term length l+1. 相似文献
15.
Harris and Keane [Probab. Theory Related Fields 109 (1997) 27-37] studied absolute continuity/singularity of two probabilities on the coin-tossing space, one representing independent tosses of a fair coin, while in the other a biased coin is tossed at renewal times of an independent renewal process and a fair coin is tossed at all other times. We extend their results by allowing possibly different biases at the different renewal times. We also investigate the contiguity and asymptotic separation properties in this kind of set-up and obtain some sufficient conditions.Keywords:renewal process, absolute continuity, singularity, contiguity, asymptotic separation, martingale convergence theorem 相似文献
16.
《Quaestiones Mathematicae》2013,36(6):789-792
AbstractIn this note, we provide a generalization of a well-known result of module theory which states that two injective modules are isomorphic when they are isomorphic to submodules of each other. More precisely, we show here that two RD-injective (respectively, pure-injective) modules over an integral domain are isomorphic if they are isomorphic to relatively divisible (respectively, pure) sub- modules of each other. 相似文献
17.
Wolfgang Rump 《Journal of Pure and Applied Algebra》2007,211(2):383-391
Let Λ be an order over a Dedekind domain R with quotient field K. An object of , the category of R-projective Λ-modules, is said to be fully decomposable if it admits a decomposition into (finitely generated) Λ-lattices. In a previous article [W. Rump, Large lattices over orders, Proc. London Math. Soc. 91 (2005) 105-128], we give a necessary and sufficient criterion for R-orders Λ in a separable K algebra A with the property that every is fully decomposable. In the present paper, we assume that is separable, but that the p-adic completion Ap is not semisimple for at least one . We show that there exists an , such that KL admits a decomposition KL=M0⊕M1 with finitely generated, where L∩M1 is fully decomposable, but L itself is not fully decomposable. 相似文献
18.
Pavel Pyrih 《Potential Analysis》1994,3(3):273-281
We study the set of functions in quasi-analytic classes and the set of finely holomorphic functions. We show that no one of these two sets is contained in the other.LetI denote the set of complex functionsf: for which there exists a quasi-analytic classC{M
n} containingf. Let denote the set of complex functionsf: for which there exist a fine domainU containing the real line and a function
finely holomorphic onU satisfyingf(x)=
(x) for allx . The power of unique continuation is incomparable in these two cases (I\ is non-empty, \I is non-empty).Research supported by the grant No. 201/93/2174 of Czech Grant Agency and by the grant No. 354 of Charles University. 相似文献
19.
Richard A. Vitale 《Acta Appl Math》1987,9(1-2):97-102
Using the expectation of a particular random set, we present a multivariate extension of a characterization theorem involving extreme order statistics.Supported in part by National Science Foundation grant DMS 8603944. 相似文献