Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-13T06:28:27.899Z Has data issue: false hasContentIssue false
  • English
  • Français

A generalisation of the lower radical class

Published online by Cambridge University Press:  17 April 2009

Robert McDougall
Robert McDougall
Affiliation:
School of Mathematical and Decision Sciences, Central Queensland University, Rockhampton Qld 4702, Australia e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this work we demonstrate that the lower radical class construction on a homomorphically closed class of associative rings generates a radical class for any class of associative rings. We also give a new description of the upper radical class using the construction on an appropriate generating class.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 139 - 146
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Divinsky, N., Rings and radicals, Mathematical Expositions 14 (University of Toronto Press, Toronto, Ont., 1965).Google Scholar
[2]Gardner, B.J. and Liang, Z., ‘Small and large radical classes’, Comm. Algebra 20 (1992), 2533–2551.Google Scholar
[3]McDougall, R.G., ‘On elements of the lattice of all radical classes, part I: Examples of pseudocomplements’, Comm. Algebra (to appear).Google Scholar
[4]McDougall, R.G., ‘The base semisimple class’, (submitted), Comm. Algebra.Google Scholar
[5]Puczylowski, E., ‘A note on hereditary radicals’, Acta Sci. Math. 44 (1982), 133–135.Google Scholar
[6]Snider, R.L., ‘Lattices of radicals’, Pacific J. Math. 40 (1972), 207–220.CrossRefGoogle Scholar
[7]Wiegandt, R., Radical and semisimple classes of rings, Queen's Papers in Pure and Applied Mathematics 37 (Queens University, Kingston, Ont., 1974).Google Scholar