共查询到20条相似文献,搜索用时 62 毫秒
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We construct an associative product on the symmetric module of any pre-Lie algebra L. It turns into a Hopf algebra which is isomorphic to the envelopping algebra of . Then we prove that in the case of rooted trees our construction is dual to that of Connes and Kreimer. We also show that symmetric brace algebras and pre-Lie algebras are the same. Finally, we give a similar interpretation of the Hopf algebra of planar rooted trees. To cite this article: J.-M. Oudom, D. Guin, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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A Rota–Baxter operator is an algebraic abstraction of integration, which is the typical example of a weight zero Rota–Baxter operator. We show that studying the modules over the polynomial Rota–Baxter algebra is equivalent to studying the modules over the Jordan plane, and we generalize the direct decomposability results for the -modules in [13] from algebraically closed fields of characteristic zero to fields of characteristic zero. Furthermore, we provide a classification of Rota–Baxter modules up to isomorphism based on indecomposable -modules. 相似文献
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《Comptes Rendus Mathematique》2014,352(7-8):577-581
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Let be an extension of commutative rings with identity, X an analytic indeterminate over B, and , the subring of the formal power series ring , consisting of the series with constant terms in A. In this Note we study when the ring R is Noetherian. We prove that R is Noetherian if and only if A is Noetherian and B is a finitely generated A-module. To cite this article: S. Hizem, A. Benhissi, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 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
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Zhidong Pan 《Linear algebra and its applications》2012,436(11):4251-4260
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François Labourie 《Comptes Rendus Mathematique》2010,348(9-10):503-507
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Alexis Kaporis Christos Makris George Mavritsakis Spyros Sioutas Athanasios Tsakalidis Kostas Tsichlas Christos Zaroliagis 《Journal of Discrete Algorithms》2010,8(4):373-387
We present the interpolation search B-tree (ISB-tree), a new cache-aware indexing scheme that supports update operations (insertions and deletions) in worst-case block transfers and search operations in expected block transfers, where B represents the disk block size and n denotes the number of stored elements. The expected search bound holds with high probability for a large class of (unknown) input distributions. The worst-case search bound of our indexing scheme is block transfers. Our update and expected search bounds constitute a considerable improvement over the worst-case block transfer bounds for search and update operations achieved by the B-tree and its numerous variants. This is also verified by an accompanying experimental study. 相似文献