共查询到20条相似文献,搜索用时 0 毫秒
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K. Zh. Kudaibergenov 《Siberian Advances in Mathematics》2008,18(2):118-123
We obtain some results on existence of small extensions of models of weakly o-minimal atomic theories. In particular, we find a sharp upper estimate for the Hanf number of such a theory for omitting an arbitrary family of pure types. We also find a sharp upper estimate for cardinalities of weakly o-minimal absolutely homogeneous models and a sufficient condition for absolute homogeneity. 相似文献
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Chen-Lian Chuang 《代数通讯》2017,45(7):2837-2847
Let R be a prime ring and δ a σ-derivation of R, where σ is an automorphism of R. Our aim (Theorem 1) is to determine any automorphism S of R[t;σ,δ] satisfying S(A)?R for a one-sided ideal A≠0 of R by dropping the assumption t∈R[t;σ,δ]. As an application, if R is a domain, it is shown that any X-inner automorphism of R[t;σ,δ] stabilizes R. 相似文献
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We use a counting argument to show that Ore extensions are associative. 相似文献
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It is proved that the Poisson enveloping algebra of a double Poisson-Ore extension is an iterated double Ore extension. As an application, properties that are preserved under iterated double Ore extensions are invariants of the Poisson enveloping algebra of a double Poisson-Ore extension. 相似文献
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We investigate the problem of the uniqueness of the extension of -homogeneous polynomials in Banach spaces. We show in particular that in a nonreflexive Banach space that admits contractive projection of finite rank of at least dimension 2, for every there exists an -homogeneous polynomial on that has infinitely many extensions to . We also prove that under some geometric conditions imposed on the norm of a complex Banach lattice , for instance when satisfies an upper -estimate with constant one for some , any -homogeneous polynomial on attaining its norm at with a finite rank band projection , has a unique extension to its bidual . We apply these results in a class of Orlicz sequence spaces.
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De Xu Zhou 《数学学报(英文版)》2009,25(9):1567-1582
Assume that S is an almost excellent extension of R. Using functors HomR(S,-) and -×R S, we establish some connections between classes of modules lR and lS, cotorsion pairs (AR, BR) and (AS, BS). If lS is a T-extension or (and) H-extension of lR, we show that lS is a (resp., monomorphic, epimorphic, special) preenveloping class if and only if so is lR. If (AS, BS) is a TH- extension of (AR, BR), we obtain that (AS, BS) is complete (resp., of finite type, of cofinite type, hereditary, perfect, n-tilting) if and only if so is (AR, BR). 相似文献
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I1和I2分别是环R的一个左理想和右理想,T1=R[x]和T2=R[x,x-1]分别表示多项式环和洛朗多项式环.首先给出两个例子,分别说明了T1I1不一定是T1的左理想与T2L2不一定是T2的右理想.其次给出了环的多项式扩张及洛朗扩张的理想的性质.最后证明了,若R[X](R[x,x-1])是拟-Baer环,则R也是拟-... 相似文献
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David E. Dobbs 《代数通讯》2013,41(12):4945-4957
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在此文中,我们对Strong-Armendariz环和Baer PP及PS环Ore-扩张R[x,x~(-1);α]的一些性质进行了讨论研究,并得到了一些结果.主要证明了R是Baer(PP)环当且仅当R[[x]]是Baer(PP)环及R是α-rigid环时,R是Baer(PP,PS)环当且仅当R[[x]]是Baer(PP,PS)环. 相似文献
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A. R. Nasr-Isfahani 《代数通讯》2013,41(3):1302-1320
Let R be a ring with an endomorphism α and an α-derivation δ. In this article, for a skew-Armendariz ring R we study some properties of skew polynomial ring R[x; α, δ]. In particular, among other results, we show that for an (α, δ)-compatible skew-Armendariz ring R, γ(R[x; α, δ]) = γ(R)[x; α, δ] = Ni?*(R)[x; α, δ], where γ is a radical in the class of radicals which includes the Wedderburn, lower nil, Levitzky, and upper nil radicals. We also show that several properties, including the symmetric, reversible, ZCn, zip, and 2-primal property, transfer between R and the skew polynomial ring R[x; α, δ], in case R is (α, δ)-compatible skew-Armendariz. As a consequence we extend and unify several known results. 相似文献
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By testing quotient rings, we give another viewpoint concerning the relationship between PI and Goldie properties, etc., and f-radical extensions of rings. The main result proved here is as follows: Let R be a prime algebra without nonzero nil right ideals. Suppose that R is f-radical over a subalgebra A, where f(X 1,…, X t ) is a multilinear polynomial, not an identity for p × p matrices in case char R = p > 0. Suppose that f is not power-central valued in R. Then the maximal ring of right (left) quotients of A coincides with that of R. Moreover, R is right Goldie if and only if A is. 相似文献
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Chen-Lian Chuang 《代数通讯》2013,41(2):481-502
Let R be a right Ore domain and φ a derivation or an automorphism of R. We determine the right Martindale quotient ring of the Ore extension R[t; φ] (Theorem 1.1). As an attempt to generalize both the Weyl algebra and the quantum plane, we apply this to rings R such that k[x] ? R ? k(x), where k is a field and x is a commuting variable. The Martindale Quotient quotient ring of R[t; φ] and its automorphisms are computed. In this way, we obtain a family of non-isomorphic infinite dimensional simple domains with all their automorphisms explicitly described. 相似文献
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《代数通讯》2013,41(10):5105-5116
Abstract A ring R is called left IP-injective if every homomorphism from a left ideal of R into R with principal image is given by right multiplication by an element of R. It is shown that R is left IP-injective if and only if R is left P-injective and left GIN (i.e., r(I ∩ K) = r(I) + r(K) for each pair of left ideals I and K of R with I principal). We prove that R is QF if and only if R is right noetherian and left IP-injective if and only if R is left perfect, left GIN and right simple-injective. We also show that, for a right CF left GIN-ring R, R is QF if and only if Soc(R R ) ? Soc( R R). Two examples are given to show that an IP-injective ring need not be self-injective and a right IP-injective ring is not necessarily left IP-injective respectively. 相似文献
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Feng Lianggui 《数学学报(英文版)》1997,13(2):231-238
In Section 1 of this paper, we investigate the finitely presented dimension of an essential extension for a module, and obtain results concerning an essential extension of a torsion-free module. We partially answer the question: When is an essential extension of a finitely presented module (an almost finitely presented module) also finitely presented (almost finitely presented)? In Section 2, we study theC-excellent extensions and the finitely presented dimensions. We obtain some results on the homological dimensions of matrix rings and group rings. 相似文献
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William J. Heinzer 《Journal of Pure and Applied Algebra》1982,26(2):189-190
If a valuation ring V on a simple transcendental field extension K0(X) is such that the residue field k of V is not algebraic over the residue field k0 of V0=V∩K0, then for k0 a perfect field it is shown that k is obtained from k0 by a finite algebraic followed by a simple transcendental field extension. 相似文献
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Alexey Sergeevich Gordienko 《代数通讯》2018,46(7):3014-3032
We show that if A is a finite-dimensional associative H-module algebra for an arbitrary Hopf algebra H, then the proof of the analog of Amitsur’s conjecture for H-codimensions of A can be reduced to the case when A is H-simple. (Here we do not require that the Jacobson radical of A is an H-submodule.) As an application, we prove that if A is a finite-dimensional associative H-module algebra where H is a Hopf algebra H over a field of characteristic 0 such that H is constructed by an iterated Ore extension of a finite-dimensional semisimple Hopf algebra by skew-primitive elements (e.g., H is a Taft algebra), then there exists integer PIexpH(A). In order to prove this, we study the structure of algebras simple with respect to an action of an Ore extension. 相似文献