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1.
We prove that if R is a semiprime ring and α is a partial action of an infinite cyclic group on R, then R is right Goldie if and only if R[x; α] is right Goldie if and only if R?x; α? is right Goldie, where R[x; α] (R?x; α?) denotes the partial skew (Laurent) polynomial ring over R. In addition, R?x; α? is semiprime while R[x; α] is not necessarily semiprime. 相似文献
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A. V. Lebedev 《Functional Analysis and Its Applications》2005,39(3):207-214
We study the relationship between the topological freeness of partial actions of discrete groups and faithful representations of the corresponding crossed products. 相似文献
4.
Let R be an associative ring with identity. A unital right R-module M is called “strongly finite dimensional” if Sup{G.dim (M/N) | N ≤ M} < +∞, where G.dim denotes the Goldie dimension of a module. Properties of strongly finite dimensional modules are explored. It is also proved that: (1) If R is left F-injective and semilocal, then R is left finite dimensional. (2) R is right artinian if and only if R is right strongly finite dimensional and right semiartinian. Some known results are obtained as corollaries. 相似文献
5.
Given a closed ideal I in a C*-algebra A, an ideal J (not necessarily closed) in I , a *-homomorphism α : A → M(I ) and a map L : J → A with some properties, based on earlier works of Pimsner and Katsura, we define a C*-algebra
which we call the Crossed Product by a Partial Endomorphism. We introduce the Crossed Product by a Partial Endomorphism
induced by a local homeomorphism σ : U → X where X is a compact Hausdorff space and U is an open subset of X. A bijection between the gauge invariant ideals of
and the σ, σ-1- invariant open subsets of X is showed. If (X, σ) has the property that
is topologically free for each closed σ, σ-1-invariant subset X′ of X then we obtain a bijection between the ideals of
and the open σ, σ-1-invariant subsets of X.
*Partially supported by CNPq.
**Supported by CNPq. 相似文献
6.
In this article, we give a criterion that characterizes equivalent weak crossed products. By duality, we obtain a similar result for weak crossed coproducts and, as a consequence, we find the conditions that assures the equivalence between two weak crossed biproducts. As an application, we show that the main results proved by Panaite in [12] (see also [11]), for Brzeziński's crossed products, admits a substantial reduction in the imposed conditions. 相似文献
7.
Let R be a ring, σ an injective endomorphism of R and δ a σ-derivation of R. We prove that if R is semiprime left Goldie then the same holds for the Ore extension R[x;σ,δ] and both rings have the same left uniform dimension.
Presented by S. Montgomery
Mathematics Subject Classification (2000) 16S90.
Jerzy Matczuk: Supported by the Flemish–Polish bilateral agreement BIL 01/31. 相似文献
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In this article, we are concerned with the crossed product S = R☆α G by a twisted partial action α of a group G on a ring R. We give necessary and sufficient (resp., sufficient) conditions for S to be a separable (resp., Frobenius, semisimple) extension of R. 相似文献
9.
It is shown that a ring R is semiprime right Goldie if and only if R is right nonsingular and every nonsingular right R-module M has a direct decomposition M = I⊕N, where I is injective and N is a reduced module such that N does not contain any extending submodule of infinite Goldie dimension. 相似文献
10.
We realize Leavitt path algebras as partial skew group rings and give new proofs, based on partial skew group ring theory of the Cuntz–Krieger uniqueness theorem and simplicity criteria for Leavitt path algebras. 相似文献
11.
Lizhong HUANG 《数学年刊B辑(英文版)》2022,43(2):295-306
This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system, and shows that the reduced crossed product is an inverse limit of an inverse system of Banach algebra crossed products. Also, the authors show that if the locally compact group is amenable, then the crossed product and the reduced crossed product are isometrically isomorphic. 相似文献
12.
John B. Polhill 《Designs, Codes and Cryptography》2002,25(3):299-309
There have been several recent constructions of partial difference sets (PDSs) using the Galois rings
for p a prime and t any positive integer. This paper presents constructions of partial difference sets in
where p is any prime, and r and t are any positive integers. For the case where
2$$
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many of the partial difference sets are constructed in groups with parameters distinct from other known constructions, and the PDSs are nested. Another construction of Paley partial difference sets is given for the case when p is odd. The constructions make use of character theory and of the structure of the Galois ring
, and in particular, the ring
×
. The paper concludes with some open related problems. 相似文献
13.
Let A be a semprime, right noetherian ring equipped with an automorphism α, and let B: = A[[y; α]] denote the corresponding skew power series ring (which is also semiprime and right noetherian). We prove that the Goldie ranks of A and B are equal. We also record applications to induced ideals. 相似文献
14.
Hiroki Matui 《Journal of Functional Analysis》2002,192(2):562-580
We will show that the crossed products of unital simple real rank zero AT algebras by the integers are AF embeddable. This is a generalization of Brown's AF embedding theorem. As an application, we will prove the AF embeddability of crossed product algebras arising from certain minimal dynamical systems induced by two commuting homeomorphisms. 相似文献
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We determine the number of edges of the finite direct product of finite rings. We apply this result to finite rings without idempotents, in particular direct products of ? m . 相似文献
17.
主要研究作用在n维欧氏空间R~n上的离散交叉积■_n■_αG_A,b_1,…,b_n的代数性质与因子分类.首先证明了该交叉积是内射的;其次给出了该交叉积为因子的一些充要条件;最后讨论该交叉积为因子时究竟是几型因子. 相似文献
18.
Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra, ln this paper, we characterize the projectivity (injectivity) of M as a left A#σ H-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σ H, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative. 相似文献
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Wagner Cortes 《代数通讯》2013,41(4):1526-1548
In this article we consider rings R with a partial action α of an infinite cyclic group G on R. We generalize the well-known results about Jacobson rings and strongly Jacobson rings in skew polynomial rings and skew Laurent polynomial rings to partial skew polynomial rings and partial skew Laurent polynomial rings. 相似文献