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On coatoms of the lattice of matric-extensible radicals
Published online by Cambridge University Press: 17 April 2009
Extract
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