*Bull. Austral. Math. Soc.* 72(3) pp.403--406, 2005.

# On coatoms of the lattice of matric-extensible radicals

## Halina France-Jackson |

.

## Abstract

A radical in the universal class of all associative
rings is called matric-extensible if for all natural numbers

*n*and all rings*A*,*A*if and only if*M*_{n}(*A*) , where*M*_{n}(*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.#### Click to download PDF of this article (free access until July 2006)

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(Metadata: XML, RSS, BibTeX) | MathSciNet: MR2199642 | Z'blatt-MATH: 1098.16010 |

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ISSN 0004-9727