Web Access Research Portal

Researcher: Gardner, BJ (Dr Barry Gardner)

Fields of Research

Algebra and number theory
Group theory and generalisations
Topology
Operator algebras and functional analysis
Theory of computation
Computational logic and formal languages
Information systems
Algebraic and differential geometry

Research Objectives

Expanding knowledge in the mathematical sciences
Mobile technologies and communications
Other information and communication services
Expanding knowledge in the physical sciences

Career Best Publications

Directoids and directed groups; Algebra Universalis
Morphic orthogonality and radicals in categories; Rings and Radicals
On product-closed radical classes of abelian groups; Bulletin Academy of Science Republic Moldova
Radical Theory of Rings; Marcel Dekker Inc

Research Publications

A note on Mal'tsev-Neumann products of radical classes; International Electronic Journal of Algebra
Closure rings; Commentationes Mathematicae Univesitatis Carolinae
Commutative quasiregular rings with isomorphic additive and circle composition groups, II: rational algebras; Communications in Algebra
Directoid groups; Czechoslovak Mathematical Journal
Directoids and directed groups; Algebra Universalis
Elementary radical classes; International Electronic Journal of Algebra
Fossicking for Finite Fields; Mathematics Magazine
Further remarks on elementary radicals and associated filters of ideals; Bulletin of the Australian Mathematical Society
Generalized higher derivations; Bulletin of the Australian Mathematical Society
Ideal Chains in Radical Theory; Acta Mathematica Hungarica
Invariant radicals; Proceedings of the Royal Society of Edinburgh
Kurosh-Amitsur radical theory for groups; Universitatea "Ovidius" Constanta. Analele. Seria Matematica
Later developments based on some ideas of Andrunachievici: Special radicals and The Lemma; Buletinul Academia de Stiinte a Republicii Moldova. Matematica
Morphic orthogonality and radicals in categories; Rings and Radicals
On product-closed radical classes of abelian groups; Bulletin Academy of Science Republic Moldova
On the Base Radical Class for Associative Rings; Acta Mathematica Hungarica
Quasiregular torsion rings having isomorphic additive and circle composition groups; Quaestiones Mathematicae
Radical classes closed under products; Analele Stiintifice ale Universitatii Ovidius Constanta
Radical Theory of Rings; Marcel Dekker Inc
Radicalizers; Communications in Algebra
Radicals and generalizations of derivations; Buletinul Academiei de Stiinte a Republicii Moldova. Matematica.
Radicals and idempotents I; Communications in Algebra
Rings and radicals; Longman
Rings in which every infinite subset contains a pair of elements with zero product; Mathematica Pannonica
Self-pseudoprojective completely decomposable abelian groups; Mathematica Pannonica
Single Elements; Beitrage zur Algebra und Geometrie
Skew ring extensions and generalized monoid rings; Acta Mathematica Hungarica
Slenderness for rings; Vietnam Journal of Mathematics
Some classes of directoid groups; Algebra and Discrete Mathematics
Steiner triple algebras; Acta Mathematica Universitatis Comenianae
Strict Radicals and Endomorphism Rings; Acta Mathematica Hungarica
Subnormalizing extensions and D-structures; ROMAI Journal
The graded Jacobson radical of associative rings; Academia de Stiinte a Republicii Moldova. Buletinul, Matematica
The Kuratowski Closure-Complement Theorem; New Zealand Journal of Mathematics
There isn't much duality in radical theory; Algebra and Discrete Mathematics
Transfer properties in radical theory; Buletinul Academiei De Stiinte A Republicii Moldova. Matematica
Two generalizations of T-nilpotence; Algebra Colloquium

Research Projects

Graded rings and applications to codes.; Australian Research Council (ARC)

Research Candidate Supervision

A connectionist approach to equational reasoning
An investigation of the Jacobson radical of epigroup graded rings
Aspects of the circle composition operation in rings
Fairly Amenable Semigroups
Radical theory in varieties of right alternative rings
Radicals and structure theory for rings related to analysis
Structural and Combinatorial Aspects of Graded Rings with Applications
Studies in Radical Theory for Restricted Classes of Rings