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Articles 331 - 356 of 356
Full-Text Articles in Mathematics
On Transitive And Fully Transitive Abelian P-Groups, D. Carroll, Brendan Goldsmith
On Transitive And Fully Transitive Abelian P-Groups, D. Carroll, Brendan Goldsmith
Articles
It is a long standing problem of A.L.S. Corner as to whether there exists a non-transitive fully transitive Abelian p-group with finite Ulm subgroups. The principal result of this paper shows that no such group exists for a special class of p-groups if the Ulm subjgroup is the direct sum of two cyclic groups. Some results on summands of trnsitive and fully transitive groups are obtained.
The Trace Of An Abelian Group:An Application To Digraphs, J. M. Burns, Brendan Goldsmith
The Trace Of An Abelian Group:An Application To Digraphs, J. M. Burns, Brendan Goldsmith
Articles
The trace of a finite Abelian group is used to give a short proof of a result of Arlinghaus and Harary on the digraph number of such a group
On Endomorphisms And Automorphisms Of Some Pure Subgroups Of The Baer-Specker Group, A. L.S. Corner, Brendan Goldsmith
On Endomorphisms And Automorphisms Of Some Pure Subgroups Of The Baer-Specker Group, A. L.S. Corner, Brendan Goldsmith
Articles
The endomoprhism algebras of certain pure subgroups of the Baer-Specker group are investigated to answer a question of Irwin. Automorphism groups of these Abelian groups are investigated and a realization theme is established.
On Quasi-Permutation Representations Of Finite Groups, J. M. Burns, Brendan Goldsmith, B. Hartley, R. Sandling
On Quasi-Permutation Representations Of Finite Groups, J. M. Burns, Brendan Goldsmith, B. Hartley, R. Sandling
Articles
In [6], Wong defined a quasi-permutation group of degree n to be a finite group G of automorphisms of an n-dimensional complex vector space such that every element of G has non-negative integral trace. The terminology derives from the fact that if G is a finite group of permutations of a set ω of size n, and we think of G as acting on the complex vector space with basis ω, then the trace of an element g ∈ G is equal to the number of points of ω fixed by g. In [6] and [7], Wong studied the extent …
Cotorsion-Free Algebras As Endomorphism Algebras In L - The Discrete An Topological Cases., R. Gobel, Brendan Goldsmith
Cotorsion-Free Algebras As Endomorphism Algebras In L - The Discrete An Topological Cases., R. Gobel, Brendan Goldsmith
Articles
The discrete algebras A over a commutative ring R which can be realised as the full endomorphism algebra of a torsion-free R-module have been investigated by Dugas and Gobel under the additional set-theoretic axiom of constructibility, V = L. Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological algebras (which could not be handled in the previous linear algebra approach) are obtained. The results obtained are independent of the usual Zermelo-Fraenkel set theory ZFC.
The Walker Endomorphism Algebra Of A Mixed Module, Brendan Goldsmith, P. Zanardo
The Walker Endomorphism Algebra Of A Mixed Module, Brendan Goldsmith, P. Zanardo
Articles
Archimedian valuation domains R are characterised in terms of the endomorphism algebras of non-splitting mixed modules of rank 1, in the Walker category.
The Kaplansky Test Problems - An Approach Via Radicals, R. Gobel, Brendan Goldsmith
The Kaplansky Test Problems - An Approach Via Radicals, R. Gobel, Brendan Goldsmith
Articles
The existence of non-free, K-free Abelian groups and modules (over some non-left perfect rings R) having prescribed endomorphism algebra is established within ZFC + 0 set theory. The principal technique used exploits free resolutions of non-free R-modules X and is similar to that used previously by Griffith and Eklof; much stronger results than have been obtained heretofore are obtained by coding additional information into the module X. As a consequence we can show, inter alia, that the Kaplansky Test Problems have negative answers for strongly K,-free Abelian groups of cardinality K1 in ZFC and assuming the weak Continuum Hypothesis.
Shadow Casting Phenomena At Newgrange, Frank Prendergast
Shadow Casting Phenomena At Newgrange, Frank Prendergast
Articles
A digital model of the Newgrange passage tomb and surrounding ring of monoliths known as the Great Circle is used to investigate sunrise shadow casting phenomena at the monument. Diurnal variation in shadow directions and lengths are analysed for their potential use in the Bronze Age to indicate the passage of seasonal time. Computer-aided simulations are developed from a photogrammetric survey to accurately show how three of the largest monoliths, located closest to the tomb entrance and archaeologically coded GC1, GC-1 and GC-2, cast their shadows onto the vertical face of the entrance kerbstone, coded K1. The phenomena occur at …
On Separable Torsion- Free Modules Of Countable Density Character, R. Gobel, Brendan Goldsmith
On Separable Torsion- Free Modules Of Countable Density Character, R. Gobel, Brendan Goldsmith
Articles
The endomorphism algebras of modules of large cardinalities have been extensively studied in recent years using the combinatorial set-theoretic techniques of Shelah-the so-called black-box methods (see, e.g., [4, 5, 151). Despite the spectacular success of these methods, they are not suitable for realization theorems at small carinalities. Of course at the level of countability (or rather more generally for cardinals ~2’~) there are in some cases the original dramatic results of A. L. S. Corner [ 1, 2, 31 and the more recent generalizations of Gobel and May [ 111. Very recently the study of realization problems at cardinalities
Mixed Modules In L, R. Gobel, Brendan Goldsmith
Mixed Modules In L, R. Gobel, Brendan Goldsmith
Articles
By assuming the set-theoretic hypothesis V = L we show that, for a large class of rings R, there exist, for any regular not weekly compact cardinals K, strongly k-cyclic mixed R-modules having endomorphism algebra isomorphic to the split extension of the R-algebra A by the ideal of bounded endomorphism provided A is free qua R-module and K./Az/
On Almost-Free Modules Over Complete Discrete Valuation Rings, Brendan Goldsmith, R. Gobel
On Almost-Free Modules Over Complete Discrete Valuation Rings, Brendan Goldsmith, R. Gobel
Articles
No abstract available
Maximal Order Abelian Subgroups Of Symmetric Groups, J. M. Burns, Brendan Goldsmith
Maximal Order Abelian Subgroups Of Symmetric Groups, J. M. Burns, Brendan Goldsmith
Articles
No abstract available
A Note On Coslender Groups, R. Dimitric, Brendan Goldsmith
A Note On Coslender Groups, R. Dimitric, Brendan Goldsmith
Articles
The notion of a coslender group has been introduced previously by the first author. This work continues the investigation of such groups, defines coslender part of a group, proves embeddability results, gives a characterization of finite rank coslender grops, and proves a result on smooth ascending chains of coslender groups with a conjecture that every countable coslender torsion free group is a smooth ascending union of finite rank coslender pure subgroups.
Essentially Indecomposable Modules Which Are Almost Free, Brendan Goldsmith, R. Gobel
Essentially Indecomposable Modules Which Are Almost Free, Brendan Goldsmith, R. Gobel
Articles
No abstract provided
On Endomorphism And Automorphisms Of Some Torsion-Free Modules, Brendan Goldsmith
On Endomorphism And Automorphisms Of Some Torsion-Free Modules, Brendan Goldsmith
Articles
The relationship between the endomorphism ring and the automorphism group of an abelian p-group has been extensively investigated. It is known that theautomorphism group need not generate the full endomorphism ring. In this paper we investigate the analagous problem for torsion free modules over a complete discrete valuation ring obtaining similar results.
Realising Rings As Endomorphism Rings: The Impact Of Logic, Brendan Goldsmith
Realising Rings As Endomorphism Rings: The Impact Of Logic, Brendan Goldsmith
Articles
No abstract available
On Endomorphism Algebras Of Mixed Modules, Brendan Goldsmith, B. Franzen
On Endomorphism Algebras Of Mixed Modules, Brendan Goldsmith, B. Franzen
Articles
No abstract available
Representations Of Algebras Over A Complete Discrete Valuation Ring, Brendan Goldsmith, Manfred Dugas, Rudiger Gobel
Representations Of Algebras Over A Complete Discrete Valuation Ring, Brendan Goldsmith, Manfred Dugas, Rudiger Gobel
Articles
No abstract available
An Essentially Semi-Rigid Class Of Modules, Brendan Goldsmith
An Essentially Semi-Rigid Class Of Modules, Brendan Goldsmith
Articles
No abstract available
Essentially Indecomposable Modules Over A Complete Discret Valuation Ring, Brendan Goldsmith
Essentially Indecomposable Modules Over A Complete Discret Valuation Ring, Brendan Goldsmith
Articles
No abstract available
A Note On Products Of Infinite Cyclic Groups, Brendan Goldsmith
A Note On Products Of Infinite Cyclic Groups, Brendan Goldsmith
Articles
In his book [2], Fuchs introduces the notion of a subgroup X of a Specker group P being a product and goes on to establish a Lemma [2, Lemma 95.1] which yields a useful characterization of the quotient and enables an easy derivation of Nunke’s characterization of epimorphic images of the Specker group [4]. Unfortunately this Lemma is incorrect as we show in section 1. In section 2 by suitably strengthening the hypothesis we regain a characterization of the quotient. Throughout, all groups are additively written Abelian groups and our notation follows the standard works of Fuchs [1], [2].
Endomorphism Rings Of Torsion-Free Modules Over A Complete Discret Valuation Ring., Brendan Goldsmith
Endomorphism Rings Of Torsion-Free Modules Over A Complete Discret Valuation Ring., Brendan Goldsmith
Articles
No abstract available.
Algorithms For The Solution Of Systems Of Coupled Second-Order Ordinary Differential Equations, Brendan O'Shea
Algorithms For The Solution Of Systems Of Coupled Second-Order Ordinary Differential Equations, Brendan O'Shea
Articles
Several step-by-step methods for the computer solution systems of coupled second-order ordinary differential equations, are examined from the point of view of efficiency “time-wise” and “storage-wise”. Particular reference is made to a system arising in the close-coupling approximation of the Schroedinger equation. The stability of the solution is also considered.
Essentially-Rigid Families Of Abelian P-Groups, Brendan Goldsmith
Essentially-Rigid Families Of Abelian P-Groups, Brendan Goldsmith
Articles
No abstract available
A Topological Approach To A Problem Of Nunke, Brendan Goldsmith
A Topological Approach To A Problem Of Nunke, Brendan Goldsmith
Articles
No abstract available
A Note On Elongations Of Abelian Groups, Brendan Goldsmith
A Note On Elongations Of Abelian Groups, Brendan Goldsmith
Articles
No abstract available.