共查询到20条相似文献,搜索用时 10 毫秒
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An infinite-dimensional N-graded k-algebra A is called projectively simple if dimkA/I<∞ for every nonzero two-sided ideal I⊂A. We show that if a projectively simple ring A is strongly noetherian, is generated in degree 1, and has a point module, then A is equal in large degree to a twisted homogeneous coordinate ring B=B(X,L,σ). Here X is a smooth projective variety, σ is an automorphism of X with no proper σ-invariant subvariety (we call such automorphisms wild), and L is a σ-ample line bundle. We conjecture that if X admits a wild automorphism then every irreducible component of X is an abelian variety. We prove several results in support of this conjecture; in particular, we show that the conjecture is true if . In the case where X is an abelian variety, we describe all wild automorphisms of X . Finally, we show that if A is projectively simple and admits a balanced dualizing complex, then is Cohen-Macaulay and Gorenstein. 相似文献
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Robert L. Snider 《Proceedings of the American Mathematical Society》1996,124(4):1043-1049
If is a finitely generated nilpotent group which is not abelian-by-finite, a field, and a finite dimensional separable division algebra over , then there exists a simple module for the group ring with endomorphism ring . An example is given to show that this cannot be extended to polycyclic groups.
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AbstractGeneralized Weyl algebras (GWAs) appear in diverse areas of mathematics including mathematical physics, noncommutative algebra, and representation theory. We study the invariants of quantum GWAs under finite order automorphisms. We extend a theorem of Jordan and Wells and apply it to determine the fixed ring of quantum GWAs under diagonal automorphisms. We further study properties of the fixed rings including global dimension, the Calabi–Yau property, rigidity, and simplicity. 相似文献
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V. K. Kharchenko 《Mathematical Notes》1975,17(6):533-536
Suppose R is a finite direct sum of simple associative rings and G is a finite group of auto-morphisms of the ring R. It is shown that if there is no additive ¦G¦-torsion in R, then the subring of elements of R that are fixed under G is a finite direct sum of simple rings. 相似文献
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A. F. Mutylin 《Mathematical Notes》1969,5(2):100-105
The paper considers a generalization to topological algebras of the concept of algebraical simplicity (see, definitions 1 and 1' below). Such topological algebras are called completely simple. Completely simple topological commutative rings and Abelian groups are described. As an appendix, a new proof is obtained for Kowalsky's theorem on fields with topologies that cannot be weakened.Translated from Matematicheskie Zametki, Vol. 5, No. 2, pp. 161–171, February, 1969.In conclusion, the author wishes to express his gratitude to his scientific director, L. A. Skornyakov. 相似文献
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We characterize right Noetherian rings over which all simple modules are almost injective. It is proved that R is such a ring, if and only if, the complements of semisimple submodules of every R-module M are direct summands of M, if and only if, R is a finite direct sum of right ideals Ir, where Ir is either a Noetherian V-module with zero socle, or a simple module, or an injective module of length 2. A commutative Noetherian ring for which all simple modules are almost injective is precisely a finite direct product of rings Ri, where Ri is either a field or a quasi-Frobenius ring of length 2. We show that for commutative rings whose all simple modules are almost injective, the properties of Kasch, (semi)perfect, semilocal, quasi-Frobenius, Artinian, and Noetherian coincide. 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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Richard Resco 《Israel Journal of Mathematics》1979,32(2-3):236-256
In this paper we prove the following theorem:
Let D be a division ring with center the field k, and let k (x
1, …, xn) denote the rational function field in n variables over k. If D contains a maximal subfield which has transcendence degree
at least n over k, then D ⊗k k (x1, …, xn) is a simple Noetherian domain of Krull and global dimensions n.
Rather surprisingly, the preceding result can be used to determine the maximum transcendence degrees of the commutative subalgebras
of several classically studied division rings. Using the theorem we prove, for example, that in the division ring of quotients
of the Weyl algebra,A
n, every maximal subfield has transcendence degree at mostn over the center. 相似文献
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Anuj Jakhar Sudesh K. Khanduja Neeraj Sangwan 《Journal of Pure and Applied Algebra》2018,222(4):889-899
Let v be a Krull valuation of a field with valuation ring . Let θ be a root of an irreducible trinomial belonging to . In this paper, we give necessary and sufficient conditions involving only for to be integrally closed. In the particular case when v is the p-adic valuation of the field of rational numbers, and , then it is shown that these conditions lead to the characterization of primes which divide the index of the subgroup in , where is the ring of algebraic integers of K. As an application, it is deduced that for any algebraic number field K and any quadratic field L not contained in K, we have if and only if the discriminants of K and L are coprime. 相似文献
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Let P be a locally finite group of prime exponent p. We prove that if P admits a finite soluble automorphism group G of order n coprime to p, such that the fixed point group C
P(G)is soluble of derived length d, then P is nilpotent of class bounded by a function of p, n, and d. A similar statement is shown to hold for Lie (p - 1)-Engel algebras; it is analogous to the Bergman-Isaacs theorem proved for associative rings, provided the condition of being soluble for an automorphism group is added. Our proof is based on a generalization of Kreknin's theorem concerning the solubility of Lie rings with a regular automorphism of finite order. This generalization, giving an affirmative answer to a question of Winter and extending one of his results to the case of infinitedimensional Lie algebras, is interesting in its own right. Moreover, we use a generalization of Higgins' theorem on the nilpotency of soluble Lie Engel algebras.
Translated fromAlgebra i Logika, Vol. 34, No. 6, pp. 706-723, November-December, 1995.Supported by RFFR grant No. 94-01-00048-a and by ISF grant NQ7000. 相似文献
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The exchange property for purely infinite simple rings 总被引:4,自引:0,他引:4
Pere Ara 《Proceedings of the American Mathematical Society》2004,132(9):2543-2547
It is proven that every purely infinite simple ring is an exchange ring. This result is applied to determine those Leavitt algebras that are exchange rings.
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L.J. Ratliff Jr 《代数通讯》2013,41(18):1977-2005
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H. H. Brungs H. Marubayashi E. Osmanagic 《Proceedings of the American Mathematical Society》2000,128(11):3167-3175
Let be a simple artinian ring. A valuation ring of is a Bézout order of so that is simple artinian, a Goldie prime is a prime ideal of so that is Goldie, and a prime segment of is a pair of neighbouring Goldie primes of A prime segment is archimedean if is equal to it is simple if and it is exceptional if In this last case, is a prime ideal of so that is not Goldie. Using the group of divisorial ideals, these results are applied to classify rank one valuation rings according to the structure of their ideal lattices. The exceptional case splits further into infinitely many cases depending on the minimal so that is not divisorial for