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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 Jan 1996

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 Jan 1995

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 Jan 1994

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 Jan 1993

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 Jan 1993

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 Jan 1993

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 Jan 1993

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 Jan 1991

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 Jan 1991

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 Jan 1989

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 Jan 1989

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 Jan 1989

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 Jan 1988

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 Jan 1988

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 Jan 1987

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 Jan 1986

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 Jan 1985

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 Jan 1984

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 Jan 1984

An Essentially Semi-Rigid Class Of Modules, Brendan Goldsmith

Articles

No abstract available


Essentially Indecomposable Modules Over A Complete Discret Valuation Ring, Brendan Goldsmith Jan 1983

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 Jan 1981

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 Jan 1978

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 Jan 1978

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 Jan 1978

Essentially-Rigid Families Of Abelian P-Groups, Brendan Goldsmith

Articles

No abstract available


A Topological Approach To A Problem Of Nunke, Brendan Goldsmith Jan 1978

A Topological Approach To A Problem Of Nunke, Brendan Goldsmith

Articles

No abstract available


A Note On Elongations Of Abelian Groups, Brendan Goldsmith Jan 1975

A Note On Elongations Of Abelian Groups, Brendan Goldsmith

Articles

No abstract available.