共查询到20条相似文献,搜索用时 46 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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If a vertex operator algebra satisfies , , then has a commutative (nonassociative) algebra structure called Griess algebra. One of the typical examples of commutative (nonassociative) algebras is a Jordan algebra. For example, the set of symmetric matrices of degree d becomes a Jordan algebra. On the other hand, in the theory of vertex operator algebras, central charges influence the properties of vertex operator algebras. In this paper, we construct vertex operator algebras with central charge c and its Griess algebra is isomorphic to for any complex number c and a positive integer d. 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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Motivated by Weyl algebra analogues of the Jacobian conjecture and the tame generators problem, we prove quantum versions of these problems for a family of analogues to the Weyl algebras. In particular, our results cover the Weyl–Hayashi algebras and tensor powers of a quantization of the first Weyl algebra which arises as a primitive factor algebra of . 相似文献
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Tathagata Basak 《Journal of Pure and Applied Algebra》2018,222(10):3036-3042
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A.L. Agore 《Journal of Pure and Applied Algebra》2018,222(4):914-930
We classify all Hopf algebras which factor through two Taft algebras and respectively . To start with, all possible matched pairs between the two Taft algebras are described: if then the matched pairs are in bijection with the group of d-th roots of unity in k, where while if then besides the matched pairs above we obtain an additional family of matched pairs indexed by . The corresponding bicrossed products (double cross product in Majid's terminology) are explicitly described by generators and relations and classified. As a consequence of our approach, we are able to compute the number of isomorphism types of these bicrossed products as well as to describe their automorphism groups. 相似文献
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Jarnishs Beltran Marco Farinati Enrique G. Reyes 《Journal of Pure and Applied Algebra》2018,222(8):2006-2021
We describe the space of central extensions of the associative algebra of formal pseudo-differential symbols in independent variables using Hochschild (co)homology groups: we prove that the first Hochschild (co)homology group is 2n-dimensional and we use this fact to calculate the first Lie (co)homology group of equipped with the Lie bracket induced by its associative algebra structure. As an application, we use our calculations to provide examples of infinite-dimensional quadratic symplectic Lie algebras. 相似文献
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Ryan Alweiss 《Discrete Mathematics》2018,341(4):981-989
The generalized Ramsey number is the smallest positive integer such that any red–blue coloring of the edges of the complete graph either contains a red copy of or a blue copy of . Let denote a cycle of length and denote a wheel with vertices. In 2014, Zhang, Zhang and Chen determined many of the Ramsey numbers of odd cycles versus larger wheels, leaving open the particular case where is even and . They conjectured that for these values of and , . In 2015, Sanhueza-Matamala confirmed this conjecture asymptotically, showing that . In this paper, we prove the conjecture of Zhang, Zhang and Chen for almost all of the remaining cases. In particular, we prove that if , , and . 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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In this paper we define odd dimensional unitary groups . These groups contain as special cases the odd dimensional general linear groups where R is any ring, the odd dimensional orthogonal and symplectic groups and where R is any commutative ring and further the first author's even dimensional unitary groups where is any form ring. We classify the E-normal subgroups of the groups (i.e. the subgroups which are normalized by the elementary subgroup ), under the condition that R is either a semilocal or quasifinite ring with involution and . Further we investigate the action of by conjugation on the set of all E-normal subgroups. 相似文献
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B.A. Sethuraman 《Journal of Pure and Applied Algebra》2018,222(11):3538-3546
Matrices A and B in are said to be mutually orthogonal if , where ? denotes the conjugate transpose. We study cardinalities of certain -linearly independent families of matrices arising from matrix embeddings of a division algebra of index m with center a number field Z, satisfying the property that matrices from different families are mutually orthogonal. The question is of importance in the context of coding for certain wireless channels, where the cardinalities of such sets is connected to the maximum code rate consistent with low decoding complexity. It follows from our results that the maximum code rate for the codes we consider is severely limited. 相似文献
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《Discrete Mathematics》2007,307(17-18):2217-2225
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《Discrete Mathematics》2006,306(10-11):886-904
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Let be a graph of order . An even squared Hamiltonian cycle (ESHC) of is a Hamiltonian cycle of with chords for all (where for ). When is even, an ESHC contains all bipartite -regular graphs of order . We prove that there is a positive integer such that for every graph of even order , if the minimum degree is , then contains an ESHC. We show that the condition of being even cannot be dropped and the constant cannot be replaced by . Our results can be easily extended to even th powered Hamiltonian cycles for all . 相似文献