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61.
Ladislav Bican 《Mathematica Slovaca》2007,57(4):333-338
In this note we are going to show that if M is a left module over a left noetherian ring R of the infinite cardinality λ ≥ |R|, then its injective hull E(M) is of the same size. Further, if M is an injective module with |M| ≥ (2λ)+ and K ≤ M is its submodule such that |M/K| ≤ λ, then K contains an injective submodule L with |M/L| ≤ 2λ. These results are applied to modules which are torsionfree with respect to a given hereditary torsion theory and generalize
the results obtained by different methods in author’s previous papers: [A note on pure subgroups, Contributions to General Algebra 12. Proceedings of the Vienna Conference, June 3–6, 1999, Verlag Johannes Heyn, Klagenfurt,
2000, pp. 105–107], [Pure subgroups, Math. Bohem. 126 (2001), 649–652].
This research has been partially supported by the Grant Agency of the Charles University, grant #GAUK 301-10/203115/B-MAT/MFF
and also by the institutional grant MSM 113 200 007. 相似文献
62.
Ladislav Bican 《Czechoslovak Mathematical Journal》2008,58(2):561-568
In the class of all exact torsion theories the torsionfree classes are cover (pre-cover) classes if and only if the classes
of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly
if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new
construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of
finite type is presented.
This research has been partially supported by the Grant Agency of the Czech Republic, grant #GAČR 201/06/0510 and also by
the institutional grant MSM 0021620839. 相似文献
63.
We present sufficient conditions on a Gaussian Mehler semigroup on a reflexive Banach space Eto be induced by a single positive symmetric operator Q \in
, and give a counterexample which shows that this representation theorem is false in every nonreflexive Banach space with a Schauder basis. We also show that the transition semigroup of a Gaussian Mehler semigroup on a separable Banach space Eacts in a pointwise continuous way, uniformly on compact subsets of E, in the space BUC(E) of bounded uniformly continuous real-valued funtions on E. The transition semigroup is shown to be strongly continuous on BUC(E) if and only if S(t) = Ifor all t 0 相似文献
64.
Let C be a connected Noetherian hereditary Abelian category with a Serre functor over an algebraically closed field k, with finite-dimensional homomorphism and extension spaces. Using the classification of such categories from our 1999 preprint, we prove that if C has some object of infinite length, then the Grothendieck group of C is finitely generated if and only if C has a tilting object. 相似文献
65.
XUXi-Xiang YANGHong-Xiang DINGHai-Yong 《理论物理通讯》2005,44(1):1-7
A difference Hamiltonian operator with three arbitrary constants is presented. When the arbitrary constants in the Hamiltonian operator are suitably chosen, a pair of Hamiltonian operators are given. The resulting Hamiltonian pair yields a difference hereditary operator. Using Magri scheme of bi-Hamiltonian formulations a hierarchy of the generalized Toda lattice equations is constructed. Finally, the discrete zero curvature representation is given for the resulting hierarchy. 相似文献
66.
Jeremy Haefner Gerald Janusz 《Transactions of the American Mathematical Society》2000,352(7):3381-3410
We characterize when a crossed product order over a maximal order in a central simple algebra by a finite group is hereditary. We need only concentrate on the cases when the group acts as inner automorphisms and when the group acts as outer automorphisms. When the group acts as inner automorphisms, the classical group algebra result holds for crossed products as well; that is, the crossed product is hereditary if and only if the order of the group is a unit in the ring. When the group is acting as outer automorphisms, every crossed product order is hereditary, regardless of whether the order of the group is a unit in the ring.
67.
S. Simons 《Transactions of the American Mathematical Society》1998,350(7):2953-2972
In this paper, we derive sufficient conditions for the sum of two or more maximal monotone operators on a reflexive Banach space to be maximal monotone, and we achieve this without any renorming theorems or fixed-point-related concepts. In the course of this, we will develop a generalization of the uniform boundedness theorem for (possibly nonreflexive) Banach spaces. We will apply this to obtain the Fenchel Duality Theorem for the sum of two or more proper, convex lower semicontinuous functions under the appropriate constraint qualifications, and also to obtain additional results on the relation between the effective domains of such functions and the domains of their subdifferentials. The other main tool that we use is a standard minimax theorem.
68.
The nonlinearity of the creep of nylon fibers is justified based on the similarity of a set of isochronous creep curves, which
also includes the instantaneous deformation curve. Nonlinear hereditary constitutive equations of creep are derived. The real
values of the influence function are determined as the basic rheological characteristic of the material. The applicability
of Boltzmann's, Abel's, Rzhanitsyn's, and Rabotnov's kernels is estimated quantitatively. The choice of an Abel-type kernel
is justified. The calculated and experimental data are in satisfactory agreement for a loading duration of up to 1,000 hours
and an order of magnitude change in the stresses
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 102–115, July 2005. 相似文献
69.
A hereditary property of combinatorial structures is a collection of structures (e.g., graphs, posets) which is closed under isomorphism, closed under taking induced substructures (e.g., induced subgraphs), and contains arbitrarily large structures. Given a property , we write for the collection of distinct (i.e., non‐isomorphic) structures in a property with n vertices, and call the function the speed (or unlabeled speed) of . Also, we write for the collection of distinct labeled structures in with vertices labeled , and call the function the labeled speed of . The possible labeled speeds of a hereditary property of graphs have been extensively studied, and the aim of this article is to investigate the possible speeds of other combinatorial structures, namely posets and oriented graphs. More precisely, we show that (for sufficiently large n), the labeled speed of a hereditary property of posets is either 1, or exactly a polynomial, or at least . We also show that there is an initial jump in the possible unlabeled speeds of hereditary properties of posets, tournaments, and directed graphs, from bounded to linear speed, and give a sharp lower bound on the possible linear speeds in each case. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 311–332, 2007 相似文献
70.
Douglas S. Bridges Hajime Ishihara Maarten McKubre‐Jordens 《Mathematical Logic Quarterly》2013,59(4-5):352-356
We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the Milman‐Pettis theorem that uniformly convex Banach spaces are reflexive. 相似文献