共查询到20条相似文献,搜索用时 15 毫秒
1.
R.R. Andruszkiewicz 《Quaestiones Mathematicae》2018,41(4):483-491
The first example of a finite rank torsion-free abelian group A such that the quotient group of A modulo the square subgroup of A is not a nil-group is indicated (in both cases of associative and general rings). In particular, the answer to the question posed by A.E. Stratton and M.C. Webb in [18], Abelian groups, nil modulo a subgroup, need not have nil quotient group, Publ. Math. Debrecen. 27 (1980), 127–130, is given for finite rank torsion-free groups. A relationship between nontrivial p-pure subgroups of the additive group of p-adic integers and nontrivial ? [p?1]-submodules of the field of p-adic numbers is investigated. In particular, a bijective correspondence between these structures is proven using only elementary methods. 相似文献
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Isidore Fleischer 《Algebra Universalis》1980,10(1):130-132
Letk be any finite or infinite cardinal andS
ω
the symmetric group of denumerable infinite degree. It is shown that fori<k ifG
i
is thei-th row of a matrix whose columns are allk-termed sequences of elements ofS
ω
in each of which all but a finite number of terms are equal to the identity ofS
ω
thenG
i
's (withG
i
−1
's defined in an obvious way and with coordinatewise multiplication amongG
i
's andG
i
−1's) generate the Free Group onk free generatorsG
i
. Analogously, Free Abelian and other types of free groups are also constructed.
Presented by L. Fuchs. 相似文献
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We define and study a notion of ring of formal power series with exponents in a cyclically ordered group. Such a ring is a quotient of various subrings of classical formal power series rings. It carries a two variable valuation function. In the particular case where the cyclically ordered group is actually totally ordered, our notion of formal power series is equivalent to the classical one in a language enriched with a predicate interpreted by the set of all monomials.Received: 24 February 2003 相似文献
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Abraham A. Ungar 《Aequationes Mathematicae》1994,47(2-3):240-254
The group of all holomorphic automorphisms of the complex unit disk consists of Möbius transformations involving translation-like holomorphic automorphisms and rotations. The former are calledgyrotranslations. As opposed to translations of the complex Plane, which are associative-commutative operations forming a group, gyrotranslations of the complex unit disk fail to form a group. Rather, left gyrotranslations are gyroassociative-gyrocommutative operations forming agyrogroup. 相似文献
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Ludwig Reich 《Aequationes Mathematicae》1985,29(1):44-49
Ohne Zusammenfassung
Herrn Professor Dr János Aczél zum 60. Geburtstag gewidmet 相似文献
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L. Babai 《Periodica Mathematica Hungarica》1980,11(4):257-270
With five exceptions, every finite regular permutation group occurs as the automorphism group of a digraph.One of the corollaries: given a finite groupG of ordern, there is a commutative semigroupS of order 2n+2 such that AutSG. The problem whether a latticeL of order Cn with AutLG exists (for some constantC), remains open. 相似文献
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We show that an isomorphism between the graphs of two simple polytopes of arbitrary dimension can always be extended to an isomorphism between the polytopes themselves. It has been convenient to study the dual situation, involving what we like to call the puzzle of a simplicial polytope.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday. 相似文献
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Atournament regular representation (TRR) of an abstract groupG is a tournamentT whose automorphism group is isomorphic toG and is a regular permutation group on the vertices ofT. L. Babai and W. Imrich have shown that every finite group of odd order exceptZ
3 ×Z
3 admits a TRR. In the present paper we give several sufficient conditions for an infinite groupG with no element of order 2 to admit a TRR. Among these are the following: (1)G is a cyclic extension byZ of a finitely generated group; (2)G is a cyclic extension byZ
2n+1 of any group admitting a TRR; (3)G is a finitely generated abelian group; (4)G is a countably generated abelian group whose torsion subgroup is finite. 相似文献
15.
Liviu C. Florescu 《Aequationes Mathematicae》1989,38(2-3):123-145
Summary In this paper we try to argue that it is necessary to replace the topological convergence structure of Menger spaces with an appropriate probabilistic concept of convergence. 相似文献
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The shift action on the 2-cocycle group Z2(G,C) of a finite group G with coefficients in a finitely generated abelian group C has several useful applications in combinatorics and digital communications, arising from the invariance of a uniform distribution property of cocycles under the action. In this article, we study the shift orbit structure of the coboundary subgroup B2(G,C) of Z2(G,C). The study is placed within a well-known setting involving the Loewy and socle series of a group algebra over G. We prove new bounds on the dimensions of terms in such series. Asymptotic results on the size of shift orbits are also derived; for example, if C is an elementary abelian p-group, then almost all shift orbits in B2(G,C) are maximal-sized for large enough finite p-groups G of certain classes. 相似文献
17.
Erwin Schörner 《Journal of Geometry》2003,78(1-2):125-155
In this paper, we generalize the results of [12]
and derive criteria for the regular embeddability
of a uniformly valued ternary field into an appropriate
Hahn ternary field of formal power series with coefficients
in the residue ternary field and exponents in the value loop.
Furthermore, we discuss these criteria also for richer
algebraic structures and we give an example for the
skew field case. 相似文献
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Christian U. Jensen Søren Jøndrup Anders Thorup 《Journal of Pure and Applied Algebra》2019,223(5):1869-1896
Classical results concerning slenderness for commutative integral domains are generalized to commutative rings with zero divisors. This is done by extending the methods from the domain case and bringing them in connection with results on the linear topologies associated to non-discrete Hausdorff filtrations. In many cases a weakened notion “almost slenderness” of slenderness is appropriate for rings with zero divisors. Special results for countable rings are extended to rings said to be of “bounded type” (including countable rings, ‘small’ rings, and, for instance, rings that are countably generated as algebras over an Artinian ring).More precisely, for a ring R of bounded type it is proved that R is slender if R is reduced and has no simple ideals, or if R is Noetherian and has no simple ideals; moreover, R is almost slender if R is not perfect (in the sense of H. Bass). We use our methods to study various special classes of rings, for instance von Neumann regular rings and valuation rings. Among other results we show that the following two rings are slender: the ring of Puiseux series over a field and the von Neumann regular ring over a von Neumann regular ring k.For a Noetherian ring R we prove that R is a finite product of local complete rings iff R satisfies one of several (equivalent) conditions of algebraic compactness. A 1-dimensional Noetherian ring is outside this ‘compact’ class precisely when it is almost slender. For the rings of classical algebraic geometry we prove that a localization of an algebra finitely generated over a field is either Artinian or almost slender. Finally, we show that a Noetherian ring R is a finite product of local complete rings with finite residue fields exactly when there exists a map of R-algebras vanishing on . 相似文献
20.
Gary Brookfield 《Journal of Pure and Applied Algebra》2005,195(3):225-230
We characterize, in terms of properties of homogeneous elements, when a graded domain is pre-Schreier or Schreier. As a consequence, the following properties of a commutative monoid domain A[M] are equivalent: (1) A[M] is pre-Schreier; (2) A[M] is Schreier; (3) A and M are Schreier. This is in contrast to pre-Schreier monoids and pre-Schreier integral domains, which need not be Schreier. 相似文献