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81.
Brian Conrad 《Compositio Mathematica》1999,119(3):239-326
Let A be a complete characteristic (0,p) discrete valuation ring with absolute ramification degree e and a perfect residue field. We are interested in studying the category FF
A' of finite flat commutative group schemes over A withp-power order. When e= 1, Fontaine formulated the purely linear algebra notion of a finite Honda system over A and constructed an anti-equivalence of categories betweenineFF
A'> and the category of finite Honda systems over A when p> 2. We generalize this theory to the case e – 1. 相似文献
82.
Let R be a ring and M a right R-module. M is called -cofinitely supplemented if every submodule N of M with M/N finitely generated has a supplement that is a direct summand of M. In this paper various properties of the -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of -cofinitely supplemented modules is -cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R-module is -cofinitely supplemented. In addition, if M has the summand sum property, then M is -cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of M. 相似文献
83.
ZhiXiangWU 《数学学报(英文版)》2004,20(1):125-134
In this paper.we study the ring #(D.B)and obtain two very interesting results. First we prove in Theorem 3 that the category of rational left BU-modules is equivalent to both the category of #-rational left modules and the category of all(B.D)-Hopf modules BM^D.Cai and Chen have proved this result in the case B=D=A.Secondly they have proved that if A has a nonzero left integral then A#A^*rat is a dense subring of Endk(A).We prove that #(A,A) is a dense subring of Endk(Q),where Q is a certain subspace of #(A.A)under the condition that the antipode is bijective(see Theorem18).This condition is weaker than the condition that A has a nonzero integral.It is well known the antipode is bijective in case A has a nonzero integral.Furthermore if A has nonzero left integral,Q can be chosen to be A(see Corollary 19)and #(A,A)is both left and right primitive.Thus A#A^*rat #(A,A)-Endk(A).Moreover we prove that the left singular ideal of the ring #(A,A)is zero.A corollary of this is a criterion for A with nonzero left integral to be finite-dimensional,namely the ring #(A,A)has a finite uniform dimension. 相似文献
84.
David Masson 《Designs, Codes and Cryptography》2003,28(3):283-302
We study (generalized) designs supported by words of given composition. We characterize them in terms of orthogonality relations with Specht modules; we define some zonal functions for the symmetric group and we give a closed formula for them, indexed on ordered pair of semi-standard generalized tableaux: Hahn polynomials are a particular case. We derive an algorithm to test if a set is a design. We use it to search designs in some ternary self-dual codes. 相似文献
85.
86.
It is well-known that every quasi-p-injective module has C2-condition. In this note, it is shown that for a quasi-p-injective module M which is a self-generator, if M is projective, duo and semiperfect, then M is continuous. As a special case we re-obtain a result of Puninski-Wisbauer-Yousif saying that, a semiperfect ring R is right continuous if it is right duo, right p-injective.AMS Subject Classifications (1991): 16D50, 16D70, 16D80Supported by The Royal Golden Jubilee Project 相似文献
87.
Using multiplication algebras we introduce actor crossed modules of commutative algebras and use it to generalise some aspects from commutative algebras to crossed modules of commutative algebras. This is applied to the Peiffer pairings in the Moore complex of a simplicial commutative algebra. 相似文献
88.
Simion Breaz 《Czechoslovak Mathematical Journal》2003,53(2):479-489
We present general properties for almost-flat modules and we prove that a self-small right module is almost flat as a left module over its endomorphism ring if and only if the class of g-static modules is closed under the kernels. 相似文献
89.
We investigate the minimal number of generators and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the semigroup. The main result is that for every bound C there exist, up to isomorphism, only finitely many divisorial ideals I such that (I)C. It follows that there exist only finitely many Cohen–Macaulay divisor classes. Moreover, we determine the minimal depth of all divisorial ideals and the behaviour of and depth in arithmetic progressions in the divisor class group.The results are generalized to more general systems of linear inequalities whose homogeneous versions define the semigroup in a not necessarily irredundant way. The ideals arising this way can also be considered as defined by the nonnegative solutions of an inhomogeneous system of linear diophantine equations.We also give a more ring-theoretic approach to the theorem on minimal number of generators of divisorial ideals: it turns out to be a special instance of a theorem on the growth of multigraded Hilbert functions. 相似文献
90.
BRST resolution is studied for the principally graded Wakimoto module of
recently found in math.QA/0005203. The submodule structure is completely determined and irreducible representations can be obtained as the zero-th cohomology group. 相似文献