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

On coatoms of the lattice of matric-extensible radicals

Halina France-Jackson

Received: 4th July, 2005

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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 Mn (A) , 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.

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

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