共查询到20条相似文献,搜索用时 15 毫秒
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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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Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
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Vladimir Shchigolev 《Journal of Algebra》2009,321(5):1453-1462
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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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Marcel Herzog Patrizia Longobardi Mercede Maj 《Journal of Pure and Applied Algebra》2018,222(7):1628-1642
Denote the sum of element orders in a finite group G by and let denote the cyclic group of order n. Suppose that G is a non-cyclic finite group of order n and q is the least prime divisor of n. We proved that and . The first result is best possible, since for each , k odd, there exists a group G of order n satisfying and the second result implies that if G is of odd order, then . Our results improve the inequality obtained by H. Amiri, S.M. Jafarian Amiri and I.M. Isaacs in 2009, as well as other results obtained by S.M. Jafarian Amiri and M. Amiri in 2014 and by R. Shen, G. Chen and C. Wu in 2015. Furthermore, we obtained some -based sufficient conditions for the solvability of G. 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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Katsunori Kawamura 《Linear algebra and its applications》2012,436(7):2638-2652
Let denote the -algebra defined as the direct sum of all matrix algebras . It is known that has a non-cocommutative comultiplication . From a certain set of transformations of integers, we construct a universal R-matrix R of the -bialgebra such that the quasi-cocommutative -bialgebra is triangular. Furthermore, it is shown that certain linear Diophantine equations are corresponded to the Yang–Baxter equations of R. 相似文献
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In this paper, we study the Galois action on the extended Bloch groups of biquadratic and dihedral number fields. We prove that if F is a biquadratic number field, then the index in Browkin and Gangl's formulas on the Brauer–Kuroda relation can only be 1 or 2. This is exactly what Browkin and Gangl predicted in their paper. Moreover we give the explicit criteria for or 2 in terms of the Tate kernels. We also prove that or p for any dihedral extension whose Galois group is the dihedral group of order 2p, where p is an odd prime. 相似文献
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In this paper, we present several necessary conditions for the reversed Dickson polynomial of the second kind to be a permutation of . In particular, we give explicit evaluation of the sum . 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