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
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.
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.Click to download PDF of this article (free access until July 2006)
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[an error occurred while processing this directive]| (Metadata: XML, RSS, BibTeX) | MathSciNet: MR2199642 | Z'blatt-MATH: 1098.16010 |
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