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On coatoms of the lattice of matric-extensible radicals

Published online by Cambridge University Press:  17 April 2009

Halina France-Jackson
Halina France-Jackson
Affiliation:
Department of Mathematics and Applied Mathematics, Summerstrand Campus (South), PO Box 77000, Nelson Mandela Metropolitan University, Port Elizabeth 6031, South Africa e-mail: [email protected]
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A radical α in the universal class of all associative rings is called matric-extensible if for all natural numbers n and all rings A, A ∈ α if and only if Mn(A) ∈ α, where Mn(A) denotes the n × n matrix ring with entries from A. We show that there are no coatoms, that is, maximal elements in the lattice of all matric-extensible radicals of associative rings.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 3 , December 2005 , pp. 403 - 406
Copyright
Copyright © Australian Mathematical Society 2005

References

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