共查询到20条相似文献,搜索用时 46 毫秒
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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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Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
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Let be an algebraically closed field of characteristic 0, and a Cohen–Macaulay graded domain with . If A is semi-standard graded (i.e., A is finitely generated as a -module), it has the h-vector, which encodes the Hilbert function of A. From now on, assume that . It is known that if A is standard graded (i.e., ), then A is level. We will show that, in the semi-standard case, if A is not level, then divides . Conversely, for any positive integers h and n, there is a non-level A with the h-vector . Moreover, such examples can be constructed as Ehrhart rings (equivalently, normal toric rings). 相似文献
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《International Journal of Approximate Reasoning》2014,55(9):1830-1842
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《Discrete Mathematics》2007,307(17-18):2235-2245
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