STRUCTURE OF RINGS VIA PSEUDO-PROJECTIVE MODULES
Abstract
In this paper, we study pseudo-projective modules over
classes of classical rings. It is shown that a ring is semilocal if and only
if every finitely generated module with Jacobson radical zero is pseudoprojective. We also give the structure of artinian principal ideal rings.
A ring is an artinian principal ideal ring if and only if the class of
pseudo-injective modules and the class of pseudo-projective modules
coincide
classes of classical rings. It is shown that a ring is semilocal if and only
if every finitely generated module with Jacobson radical zero is pseudoprojective. We also give the structure of artinian principal ideal rings.
A ring is an artinian principal ideal ring if and only if the class of
pseudo-injective modules and the class of pseudo-projective modules
coincide
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