共查询到20条相似文献,搜索用时 78 毫秒
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Diogo Diniz Claudemir Fidelis Bezerra Júnior 《Journal of Pure and Applied Algebra》2018,222(6):1388-1404
Let F be an infinite field. The primeness property for central polynomials of was established by A. Regev, i.e., if the product of two polynomials in distinct variables is central then each factor is also central. In this paper we consider the analogous property for and determine, within the elementary gradings with commutative neutral component, the ones that satisfy this property, namely the crossed product gradings. Next we consider , where R admits a regular grading, with a grading such that is a homogeneous subalgebra and provide sufficient conditions – satisfied by with the trivial grading – to prove that has the primeness property if does. We also prove that the algebras satisfy this property for ordinary central polynomials. Hence we conclude that, over a field of characteristic zero, every verbally prime algebra has the primeness property. 相似文献
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Vladimir Shchigolev 《Journal of Algebra》2009,321(5):1453-1462
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Gábor Korchmáros Maria Montanucci Pietro Speziali 《Journal of Pure and Applied Algebra》2018,222(7):1810-1826
Let be the algebraic closure of a finite field of odd characteristic p. For a positive integer m prime to p, let be the transcendence degree 1 function field defined by . Let and . The extension is a non-Galois extension. Let K be the Galois closure of F with respect to H. By Stichtenoth [20], K has genus , p-rank (Hasse–Witt invariant) and a -automorphism group of order at least . In this paper we prove that this subgroup is the full -automorphism group of K; more precisely where Δ is an elementary abelian p-group of order and D has an index 2 cyclic subgroup of order . In particular, , and if K is ordinary (i.e. ) then . On the other hand, if G is a solvable subgroup of the -automorphism group of an ordinary, transcendence degree 1 function field L of genus defined over , then ; see [15]. This shows that K hits this bound up to the constant .Since has several subgroups, the fixed subfield of such a subgroup N may happen to have many automorphisms provided that the normalizer of N in is large enough. This possibility is worked out for subgroups of Δ. 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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Cristhian E. Hidber Miguel A. Xicoténcatl 《Journal of Pure and Applied Algebra》2018,222(6):1478-1488
The purpose of this article is to compute the mod 2 cohomology of , the mapping class group of the Klein bottle with q marked points. We provide a concrete construction of Eilenberg–MacLane spaces and fiber bundles , where denotes the configuration space of unordered q-tuples of distinct points in and is the classifying space of the group . Moreover, we show the mod 2 Serre spectral sequence of the bundle above collapses. 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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A.S. Sivatski 《Journal of Pure and Applied Algebra》2018,222(3):560-567
Let F be a field of characteristic distinct from 2, a quadratic field extension. Let further f and g be quadratic forms over L considered as polynomials in n variables, , their matrices. We say that the pair is a k-pair if there exist such that all the entries of the upper-left corner of the matrices and are in F. We give certain criteria to determine whether a given pair is a k-pair. We consider the transfer determined by the -linear map with , , and prove that if , then is a -pair. If, additionally, the form does not have a totally isotropic subspace of dimension over , we show that is a -pair. In particular, if the form is anisotropic, and , then is a k-pair. 相似文献
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We investigate the following problem posed by Cabello Sanchéz, Castillo, Kalton, and Yost:Let K be a nonmetrizable compact space. Does there exist a nontrivial twisted sum of and , i.e., does there exist a Banach space X containing a non-complemented copy Y of such that the quotient space is isomorphic to ?Using additional set-theoretic assumptions we give the first examples of compact spaces K providing a negative answer to this question. We show that under Martin's axiom and the negation of the continuum hypothesis, if either K is the Cantor cube or K is a separable scattered compact space of height 3 and weight , then every twisted sum of and is trivial.We also construct nontrivial twisted sums of and for K belonging to several classes of compacta. Our main tool is an investigation of pairs of compact spaces which do not admit an extension operator . 相似文献
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Gangyong Lee Jae Keol Park S. Tariq Rizvi Cosmin S. Roman 《Journal of Pure and Applied Algebra》2018,222(9):2427-2455
Let V be a module with . V is called a quasi-Baer module if for each ideal J of S, for some . On the other hand, V is called a Rickart module if for each , for some . For a module N, the quasi-Baer module hull (resp., the Rickart module hull ) of N, if it exists, is the smallest quasi-Baer (resp., Rickart) overmodule, in a fixed injective hull of N. In this paper, we initiate the study of quasi-Baer and Rickart module hulls. When a ring R is semiprime and ideal intrinsic over its center, it is shown that every finitely generated projective R-module has a quasi-Baer hull. Let R be a Dedekind domain with F its field of fractions and let be any set of R-submodules of . For an R-module with , we show that has a quasi-Baer module hull if and only if is semisimple. This quasi-Baer hull is explicitly described. An example such that has no Rickart module hull is constructed. If N is a module over a Dedekind domain for which is projective and , where is the torsion submodule of N, we show that the quasi-Baer hull of N exists if and only if is semisimple. We prove that the Rickart module hull also exists for such modules N. Furthermore, we provide explicit constructions of and and show that in this situation these two hulls coincide. Among applications, it is shown that if N is a finitely generated module over a Dedekind domain, then N is quasi-Baer if and only if N is Rickart if and only if N is Baer if and only if N is semisimple or torsion-free. For a direct sum of finitely generated modules, where R is a Dedekind domain, we show that N is quasi-Baer if and only if N is Rickart if and only if N is semisimple or torsion-free. Examples exhibiting differences between the notions of a Baer hull, a quasi-Baer hull, and a Rickart hull of a module are presented. Various explicit examples illustrating our results are constructed. 相似文献
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Let V be an n-dimensional vector space over the finite field consisting of q elements and let be the Grassmann graph formed by k-dimensional subspaces of V, . Denote by the restriction of to the set of all non-degenerate linear codes. We show that for any two codes the distance in coincides with the distance in only in the case when , i.e. if n is sufficiently large then for some pairs of codes the distances in the graphs and are distinct. We describe one class of such pairs. 相似文献
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