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Articles 301 - 320 of 320
Full-Text Articles in Mathematics
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.