共查询到20条相似文献,搜索用时 15 毫秒
1.
Anthony J. Crachiola 《Journal of Pure and Applied Algebra》2009,213(9):1735-1738
We show that if A and B are finitely generated two-dimensional unique factorization domains over an algebraically closed field, then A[x]≅B[x] implies A≅B. The proof is an application of an algebraic technique involving the AK invariant which has previously been used to obtain other cancellation theorems. 相似文献
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We give a criterion to decide if a given w-homogeneous derivation on A?k[X1,X2,X3] is locally nilpotent. We deduce an algorithm which decides if a k-subalgebra of A, which is finitely generated by w-homogeneous elements, is the kernel of some locally nilpotent derivation. 相似文献
3.
Philippe Bonnet 《Journal of Pure and Applied Algebra》2007,210(2):383-394
Let A be an integral k-algebra of finite type over an algebraically closed field k of characteristic p>0. Given a collection D of k-derivations on A, that we interpret as algebraic vector fields on , we study the group spanned by the hypersurfaces V(f) of X invariant under D modulo the rational first integrals of D. We prove that this group is always a finite dimensional Fp-vector space, and we give an estimate for its dimension. This is to be related to the results of Jouanolou and others on the number of hypersurfaces invariant under a foliation of codimension 1. As a application, given a k-algebra B between Ap and A, we show that the kernel of the pull-back morphism is a finite Fp-vector space. In particular, if A is a UFD, then the Picard group of B is finite. 相似文献
4.
Let k be a field of characteristic zero and R a factorial affine k-domain. Let B be an affineR-domain. In terms of locally nilpotent derivations, we give criteria for B to be R-isomorphic to the residue ring of a polynomial ring R[X1,X2,Y] over R by the ideal (X1X2−φ(Y)) for φ(Y)∈R[Y]?R. 相似文献
5.
Hideo Kojima 《Journal of Pure and Applied Algebra》2011,215(10):2512-2514
Let A=R[x1,…,xn] be the polynomial ring in n variables over an integral domain R with unit, let D be a rational higher R-derivation on A and let be the extension of D to the quotient field of A. We prove that, if the transcendental degree of the kernel of D over R is not less than n−1, then the quotient field of the kernel of D equals the kernel of . Moreover, when n=2, we give a necessary and sufficient condition for an R-subalgebra of A to be expressed as the kernel of a rational higher R-derivation on A. 相似文献
6.
In this paper we show that the image of any locally finite k-derivation of the polynomial algebra k[x,y] in two variables over a field k of characteristic zero is a Mathieu subspace. We also show that the two-dimensional Jacobian conjecture is equivalent to the statement that the image of every k-derivation D of k[x,y] such that and is a Mathieu subspace of k[x,y]. 相似文献
7.
José M. Giral 《Journal of Pure and Applied Algebra》2009,213(5):601-604
The effective relations and the relation type of an ideal generated by two regular elements can be expressed in terms of the ring of global sections of the blowing-up along the ideal. As a consequence, we find the minimal overring where the ideal is syzygetic or of linear type. 相似文献
8.
Stefania Gabelli Evan Houston Thomas G. Lucas 《Journal of Pure and Applied Algebra》2004,194(3):281-298
Generalizing work of Gilmer and Heinzer, we define a t#-domain to be a domain R in which for any two distinct subsets and of the set of maximal t-ideals of R. We provide characterizations of these domains, and we show that polynomial rings over t#-domains are again t#-domains. Finally, we study overrings of t#-domains. 相似文献
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We show that in certain Prüfer domains, each nonzero ideal I can be factored as , where Iv is the divisorial closure of I and is a product of maximal ideals. This is always possible when the Prüfer domain is h-local, and in this case such factorizations have certain uniqueness properties. This leads to new characterizations of the h-local property in Prüfer domains. We also explore consequences of these factorizations and give illustrative examples. 相似文献
12.
We introduce and study the notion of ?-stability with respect to a semistar operation ? defined on a domain R; in particular we consider the case where ? is the w-operation. This notion allows us to generalize and improve several properties of stable domains and totally divisorial domains. 相似文献
13.
Duong Quôc Viê.t 《Journal of Pure and Applied Algebra》2006,205(3):498-509
Let I be an equimultiple ideal of Noetherian local ring A. This paper gives some multiplicity formulas of the extended Rees algebras T=A[It,t-1]. In the case A generalized Cohen-Macaulay, we determine when T is Cohen-Macaulay and as an immediate consequence we obtain e.g., some criteria for the Cohen-Macaulayness of Rees algebra R(I) over a Cohen-Macaulay ring in terms of reduction numbers and ideals. 相似文献
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Let R be a principal ideal domain. In this paper we prove that, for a large class of linear systems, dynamic feedback over R is equivalent to static feedback over a quotient ring of R. In particular, when R is the ring of integers Z one has that the static feedback classification problem over finite rings is equivalent to the dynamic feedback classification problem over Z restricted to a special type of system. 相似文献
16.
The purpose of this paper is to study the stable extendibility of the tangent bundle τn(p) over the (2n+1)-dimensional standard lens space Ln(p) for odd prime p. We investigate for which m the tangent bundle τn(p) is stably extendible to Lm(p) but is not stably extendible to Lm+1(p), where we consider m=∞ if τn(p) is stably extendible to Lk(p) for any k?n, and determine m in the case n?p−3. 相似文献
17.
A nonzero locally nilpotent linear derivation δ of the polynomial algebra K[Xd]=K[x1,…,xd] in several variables over a field K of characteristic 0 is called a Weitzenböck derivation. The classical theorem of Weitzenböck states that the algebra of constants K[Xd]δ (which coincides with the algebra of invariants of a single unipotent transformation) is finitely generated. Similarly one may consider the algebra of constants of a locally nilpotent linear derivation δ of a finitely generated (not necessarily commutative or associative) algebra which is relatively free in a variety of algebras over K . Now the algebra of constants is usually not finitely generated. Except for some trivial cases this holds for the algebra of constants (Ld/Ld″)δ of the free metabelian Lie algebra Ld/Ld″ with d generators. We show that the vector space of the constants (Ld/Ld″)δ in the commutator ideal Ld′/Ld″ is a finitely generated K[Xd]δ-module. For small d , we calculate the Hilbert series of (Ld/Ld″)δ and find the generators of the K[Xd]δ-module (Ld/Ld″)δ. This gives also an (infinite) set of generators of the algebra (Ld/Ld″)δ. 相似文献
18.
Christian Lundkvist 《Journal of Pure and Applied Algebra》2008,212(10):2236-2249
We investigate the similarities and differences between the module of symmetric tensors and the module of divided powers . There is a canonical map which is an isomorphism in many important cases. We give examples showing that this map need neither be surjective nor injective in general. These examples also show that the functor does not in general commute with base change. 相似文献
19.
Let F be either the real number field R or the complex number field C and RPn the real projective space of dimension n. Theorems A and C in Hemmi and Kobayashi (2008) [2] give necessary and sufficient conditions for a given F-vector bundle over RPn to be stably extendible to RPm for every m?n. In this paper, we simplify the theorems and apply them to the tangent bundle of RPn, its complexification, the normal bundle associated to an immersion of RPn in Rn+r(r>0), and its complexification. Our result for the normal bundle is a generalization of Theorem A in Kobayashi et al. (2000) [8] and that for its complexification is a generalization of Theorem 1 in Kobayashi and Yoshida (2003) [5]. 相似文献
20.
Anatoliy P. Petravchuk 《Linear algebra and its applications》2010,433(3):574-579
It is well known that each pair of commuting linear operators on a finite dimensional vector space over an algebraically closed field has a common eigenvector. We prove an analogous statement for derivations of k[x] and k[x,y] over any field k of zero characteristic. In particular, if D1 and D2 are commuting derivations of k[x,y] and they are linearly independent over k, then either (i) they have a common polynomial eigenfunction; i.e., a nonconstant polynomial f∈k[x,y] such that D1(f)=λf and D2(f)=μf for some λ,μ∈k[x,y], or (ii) they are Jacobian derivations