Rings characterised by semiprimitive modules
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説明
<jats:p>A module <jats:italic>M</jats:italic> is called a CS-module if every submodule of <jats:italic>M</jats:italic> is essential in a direct summand of <jats:italic>M</jats:italic>. It is shown that a ring <jats:italic>R</jats:italic> is semilocal if and only if every semiprimitive right <jats:italic>R</jats:italic>-module is CS. Furthermore, it is also shown that the following statements are equivalent for a ring <jats:italic>R</jats:italic>: (i) <jats:italic>R</jats:italic> is semiprimary and every right (or left) <jats:italic>R</jats:italic>-module is injective; (ii) every countably generated semiprimitive right <jats:italic>R</jats:italic>-module is a direct sum of a projective module and an injective module.</jats:p>
収録刊行物
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- Bulletin of the Australian Mathematical Society
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Bulletin of the Australian Mathematical Society 52 107-116, 1995-08-01
Cambridge University Press (CUP)
