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G. Stengle 《Journal of Pure and Applied Algebra》2011,215(9):2257-2261
Let A⊂R be rings containing the rationals. In R let S be a multiplicatively closed subset such that 1∈S and 0∉S, T a preorder of R (a proper subsemiring containing the squares) such that S⊂T and I an A-submodule of R. Define ρ(I) (or ρS,T(I)) to be
ρ(I)={a∈R|sa2m+t∈I2m for some m∈N,s∈S and t∈T}. 相似文献
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B. I. Plotkin 《Journal of Mathematical Sciences》2006,139(4):6780-6791
Let Θ be a variety of algebras. In every variety Θ and every algebra H from Θ one can consider algebraic geometry in Θ over H. We also consider a special categorical invariant K Θ of this geometry. The classical algebraic geometry deals with the variety Θ = Com-P of all associative and commutative algebras over the ground field of constants P. An algebra H in this setting is an extension of the ground field P. Geometry in groups is related to the varieties Grp and Grp-G, where G is a group of constants. The case Grp-F, where F is a free group, is related to Tarski’s problems devoted to logic of a free group. The described general insight on algebraic geometry in different varieties of algebras inspires some new problems in algebra and algebraic geometry. The problems of such kind determine, to a great extent, the content of universal algebraic geometry. For example, a general and natural problem is: When do algebras H 1 and H 2 have the same geometry? Or more specifically, what are the conditions on algebras from a given variety Θ that provide the coincidence of their algebraic geometries? We consider two variants of coincidence: 1) K Θ(H 1) and K Θ(H 2) are isomorphic; 2) these categories are equivalent. This problem is closely connected with the following general algebraic problem. Let Θ0 be the category of all algebras W = W(X) free in Θ, where X is finite. Consider the groups of automorphisms Aunt(Θ0) for different varieties Θ and also the groups of autoequivalences of Θ0. The problem is to describe these groups for different Θ. 相似文献
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Amnon Yekutieli 《Advances in Mathematics》2005,198(1):383-432
We study deformation quantizations of the structure sheaf OX of a smooth algebraic variety X in characteristic 0. Our main result is that when X is D-affine, any formal Poisson structure on X determines a deformation quantization of OX (canonically, up to gauge equivalence). This is an algebro-geometric analogue of Kontsevich's celebrated result. 相似文献
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A. G. Pinus 《Algebra and Logic》2011,50(2):146-160
We consider problems of comparing universal algebras in respect of their conditional algebraic geometries. Such comparisons
admit of a quite natural algebraic interpretation. Geometric scales for varieties of algebras constructed based on these relations
are a natural tool for classifying the varieties of algebras, discriminator varieties in particular. 相似文献
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Xiaomin Tang 《代数通讯》2017,45(12):5252-5261
In this paper, the biderivations without the skew-symmetric condition of W-algebras including the Witt algebra, the algebra W(2,2) and their central extensions are characterized. Some classes of non-inner biderivations are presented. As applications, the forms of linear commuting maps and the commutative post-Lie algebra structures on aforementioned W-algebras are given. 相似文献
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We extend the notion of a strong Ditkin set in the dual group for the \({L^1}\)-algebra of a locally compact abelian group as well as a large number of results for such sets to the setting of a general regular and semisimple commutative Banach algebra and its spectrum. In particular, we study various stability and inheritance properties. Moreover, we present some applications to Fourier algebras of locally compact groups and an example of a compact, infinite double coset hypergroup for which every closed subset is a strong Ditkin set for its Fourier algebra. 相似文献
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A. A. Mishchenko 《Algebra and Logic》2009,48(3):214-227
The results obtained deal in algebraic geometry over partially commutative class two nilpotent ℚ-groups, where ℚ is a field
of rationals. It is proved that two arbitrary non-Abelian partially commutative class two nilpotent ℚ-groups are geometrically
equivalent. A necessary and sufficient condition of being universally geometrically equivalent is specified for two partially
commutative class two nilpotent ℚ-groups. Algebraic sets for systems of equations in one variable, as well as for some special
systems in several variables, are described.
Dedicated to V. N. Remeslennikov on the occasion of his 70th birthday
Translated from Algebra i Logika, Vol. 48, No. 2, pp. 378–399, May–June, 2009. 相似文献
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Ze Min Zeng 《Journal of Pure and Applied Algebra》2006,207(1):139-147
Let A be a regular ring of dimension d (d≥3) containing an infinite field k. Let n be an integer such that 2n≥d+3. Let I be an ideal in A of height n and P be a projective A-module of rank n. Suppose P⊕A≈An+1 and there is a surjection α: P→I. It is proved in this note that I is a set theoretic complete intersection ideal. As a consequence, a smooth curve in a smooth affine C-algebra with trivial conormal bundle is a set theoretic complete intersection if its corresponding class in the Grothendieck group is torsion. 相似文献
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Bernd Sturmfels Caroline Uhler 《Annals of the Institute of Statistical Mathematics》2010,62(4):603-638
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum
likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and
to the problem of characterizing the image of the positive definite cone under an arbitrary linear projection. These problems
at the interface of statistics and optimization are here examined from the perspective of convex algebraic geometry. 相似文献
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Yum-Tong Siu 《中国科学A辑(英文版)》2005,48(Z1)
The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invari-ance of plurigenera for general compact algebraic manifolds is presented and discussed. Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed. 相似文献
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The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed. Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed.
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Ahmed Ayache 《Journal of Pure and Applied Algebra》2008,212(1):140-146
The main purpose of this paper is to establish a result giving the number of intermediary rings between R and S when (R,S) is a normal pair of rings and to provide an algorithm to compute this number. 相似文献