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《Annals of Pure and Applied Logic》2019,170(12):102719
We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideals have dense value groups. For Bézout domains, these conditions are also necessary. 相似文献
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S. Bazzoni 《代数通讯》2013,41(11):5157-5167
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Qian Guohua 《Proceedings of the American Mathematical Society》2004,132(7):1899-1903
Let be a finite group and the largest irreducible character degree of . In this note, we show the following results: if , then ; if and, in addition, is -solvable with abelian Sylow -subgroup, then .
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Abstract Let D be a Prüfer domain, and denote by ± b?(D) the multiplicative group of all invertible fractional ideals of D, ordered by A ≤ B if and only if A ? B. Denote by G i the value group of the valuation associated with the valuation ring D M i , where {M i } i∈I is the collection of all maximal ideals of D. In this note we prove that the natural map from ± b?(D) into ± b∏ i∈I G i is an isomorphism onto the cardinal sum ± b? i∈I G i if and only if D is h-local. As a corollary, the group of divisibility of an h-local Bézout domain is isomorphic to ± b? i∈I G i , the notation being as above. 相似文献
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If R is an integral domain, let be the class of torsion free completely decomposable R-modules of finite rank. Denote by the class of those torsion-free R-modules A such that A is a homomorphic image of some C ? , and let 𝒫 be the class of R-modules K such that K is a pure submodule of some C ? . Further, let Q and Q 𝒫 be the respective closures of and 𝒫 under quasi-isomorphism. In this article, it is shown that if R is a Prüfer domain, then Q = Q 𝒫, and = 𝒫 in the special case when R is h-local. Also, if R is an h-local Prüfer domain and if C ? has a linearly ordered typeset, it is established that all pure submodules and all torsion-free homomorphic images of C are themselves completely decomposable. Finally, as an application of these results, we prove that if R is an h-local Prüfer domain, then = Q = Q 𝒫 = 𝒫 if and only if R is almost maximal. 相似文献
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We prove that the finite‐model version of arithmetic with the divisibility relation is undecidable (more precisely, it has Π01‐complete set of theorems). Additionally we prove FM‐representability theorem for this class of finite models. This means that a relation R on natural numbers can be described correctly on each input on almost all finite divisibility models if and only if R is of degree ≤ 0 ′. We obtain these results by interpreting addition and multiplication on initial segments of finite models with divisibility only. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Olivier A. Heubo-Kwegna 《代数通讯》2013,41(8):2701-2719
We consider the ring Kr(F/D), where D is a subring of a field F, that is the intersection of the trivial extensions to F(X) of the valuation rings of the Zariski–Riemann space consisting of all valuation rings of the extension F/D and investigate the ideal structure of Kr(F/D) in the case where D is an affine algebra over a subfield K of F and the extension F/K has countably infinite transcendence degree, by using the topological structure of the Zariski–Riemann space. We show that for any pair of nonnegative integers d and h, there are infinitely many prime ideals of dimension d and height h that are minimal over any proper nonzero finitely generated ideal of Kr(F/D). 相似文献
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Hwankoo Kim 《代数通讯》2013,41(2):759-772
We give several module-theoretic characterizations of generalized GCD domains. For example, we show that an integral domain R is a generalized GCD domain if and only if semi-divisoriality and flatness are equivalent for torsion-free R-modules if and only if every w-finite w-module is projective if and only if R is w-Prüfer (in the sense of Zafrullah). We also characterize when a pullback R of a certain type is a generalized GCD domain. As an application, we characterize when R = D + XE[X] (here, D ? E is an extension of domains and X is an indeterminate) is a generalized GCD domain. 相似文献
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Let U be a Sylow p-subgroup of the finite Chevalley group of type D4 over the field of q elements, where q is a power of a prime p. We describe a construction of the generic character table of U. 相似文献
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Zeinab Akhlaghi 《Mathematische Nachrichten》2023,296(8):3149-3152
Let G be a finite group and N be a non-trivial normal subgroup of G, such that the average degree of irreducible characters in is less than or equal to 16/5. Then, we prove that N is solvable. Also, we prove the solvability of G, by assuming that the average degree of irreducible characters in is strictly less than 16/5. We show that the bounds are sharp. 相似文献
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D. S. Passman 《Transactions of the American Mathematical Society》1997,349(12):4693-4751
This paper is the final installment in a series of articles, started in 1974, which study the semiprimitivity problem for group algebras of locally finite groups. Here we achieve our goal of describing the Jacobson radical in terms of the radicals of the group algebras of the locally subnormal subgroups of . More precisely, we show that if and if , then the controller of is the characteristic subgroup generated by the locally subnormal subgroups of with . In particular, we verify a conjecture proposed some twenty years ago and, in so doing, we essentially solve one half of the group ring semiprimitivity problem for arbitrary groups. The remaining half is the more difficult case of finitely generated groups. This article is effectively divided into two parts. The first part, namely the material in Sections 2-6, covers the group theoretic aspects of the proof and may be of independent interest. The second part, namely the work in Sections 7-12, contains the group ring and ring theoretic arguments and proves the main result. As usual, it is necessary for us to work in the more general context of twisted group algebras and crossed products. Furthermore, the proof ultimately depends upon results which use the Classification of the Finite Simple Groups.
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V. S. Varadarajan 《Proceedings Mathematical Sciences》1987,97(1-3):305-312
Deligne’s generalization of the Hadamard—Vallée Poussin method in classical number theory is formulated as the representability
of certain states of the character ring of a compact group, and the determination of all the representable states is carried
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Research partially supported by NSF Grant 85-01742. 相似文献