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Maximal immediate extensions are not necessarily maximally complete
Published online by Cambridge University Press: 09 April 2009
Abstract
An extension R1 of a right chain ring R is called immediate if R1 has the same residue division ring and the same lattice of principal right ideals as R. Properties of such immediate extensions are studied. It is proved that for every R, maximal immediate extensions exist, but that in contrast to the commutative case maximal right chain rings are not necessarily linearly compact.
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- Research Article
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- Copyright © Australian Mathematical Society 1990
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