共查询到20条相似文献,搜索用时 31 毫秒
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Hüseyi̇n Çakallı 《Mathematical and Computer Modelling》2011,53(1-2):397-401
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Let A be a unital algebra and M be a unital A-bimodule. A linear map δ : A →M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ(A) ? B + A ? δ(B) =δ(A ? B) for any A, B ∈ A with A ? B = P, here A ? B = AB + BA is the usual Jordan product. In this article, we show that if A = Alg N is a Hilbert space nest algebra and M = B(H), or A = M = B(X), then, a linear map δ : A → M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P ∈ B(X) if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained. 相似文献
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Akaki Tikaradze 《Journal of Pure and Applied Algebra》2017,221(1):229-236
Let k be a perfect field of characteristic . Let be an Azumaya algebra over a smooth symplectic affine variety over k. Let be a deformation quantization of over . We prove that all -flat two-sided ideals of are generated by central elements. 相似文献
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Zhidong Pan 《Linear algebra and its applications》2012,436(11):4251-4260
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Mi Hee Park Byung Gyun Kang Phan Thanh Toan 《Journal of Pure and Applied Algebra》2018,222(8):2299-2309
Let be the power series ring over a commutative ring R with identity. For , let denote the content ideal of f, i.e., the ideal of R generated by the coefficients of f. We show that if R is a Prüfer domain and if such that is locally finitely generated (or equivalently locally principal), then a Dedekind–Mertens type formula holds for g, namely for all . More generally for a Prüfer domain R, we prove the content formula for all . As a consequence it is shown that an integral domain R is completely integrally closed if and only if for all nonzero , which is a beautiful result corresponding to the well-known fact that an integral domain R is integrally closed if and only if for all nonzero , where is the polynomial ring over R.For a ring R and , if is not locally finitely generated, then there may be no positive integer k such that for all . Assuming that the locally minimal number of generators of is , Epstein and Shapiro posed a question about the validation of the formula for all . We give a negative answer to this question and show that the finiteness of the locally minimal number of special generators of is in fact a more suitable assumption. More precisely we prove that if the locally minimal number of special generators of is , then for all . As a consequence we show that if is finitely generated (in particular if ), then there exists a nonnegative integer k such that for all . 相似文献
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Dawid Tarłowski 《Operations Research Letters》2018,46(1):33-36
Let be a continuous function with the minimal value , where is the compact metric space. Let be a Markov chain which represents the global optimization process on . We present sufficient conditions for very strong, geometric convergence mode of the form , where is some constant. This convergence mode is natural if the set of global minima is fat. 相似文献
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This paper develops systematically the stochastic calculus via regularization in the case of jump processes. In particular one continues the analysis of real-valued càdlàg weak Dirichlet processes with respect to a given filtration. Such a process is the sum of a local martingale and an adapted process such that , for any continuous local martingale . Given a function , which is of class (or sometimes less), we provide a chain rule type expansion for which stands in applications for a chain Itô type rule. 相似文献
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An approximation scheme is a family of homogeneous subsets of a quasi-Banach space , such that , , and . Continuing the line of research originating at the classical paper [8] by Bernstein, we give several characterizations of the approximation schemes with the property that, for every sequence , there exists such that (in this case we say that satisfies Shapiro’s Theorem). If is a Banach space, as above exists if and only if, for every sequence , there exists such that . We give numerous examples of approximation schemes satisfying Shapiro’s Theorem. 相似文献
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Let D be a commutative domain with field of fractions K, let A be a torsion-free D-algebra, and let B be the extension of A to a K-algebra. The set of integer-valued polynomials on A is , and the intersection of with is , which is a commutative subring of . The set may or may not be a ring, but it always has the structure of a left -module.A D-algebra A which is free as a D-module and of finite rank is called -decomposable if a D-module basis for A is also an -module basis for ; in other words, if can be generated by and A. A classification of such algebras has been given when D is a Dedekind domain with finite residue rings. In the present article, we modify the definition of -decomposable so that it can be applied to D-algebras that are not necessarily free by defining A to be -decomposable when is isomorphic to . We then provide multiple characterizations of such algebras in the case where D is a discrete valuation ring or a Dedekind domain with finite residue rings. In particular, if D is the ring of integers of a number field K, we show that an -decomposable algebra A must be a maximal D-order in a separable K-algebra B, whose simple components have as center the same finite unramified Galois extension F of K and are unramified at each finite place of F. Finally, when both D and A are rings of integers in number fields, we prove that -decomposable algebras correspond to unramified Galois extensions of K. 相似文献