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| Paper IPM / M / 8001 |
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| Abstract: | |
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Let R be a ring with identity and let M be a unitary right
R-module. Then, M is essentially compressible provided M
embeds in every essential submodule of M. It is proved that
every nonsingular essentially compressible module M is
isomorphic to a submodule of a free module, and the converse holds
in case R is semiprime right Goldie. In case R is a right FBN
ring, M is essentially compressible if and only if M is
subisomorphic to a direct sum of critical compressible modules.
The ring R is right essentially compressible if and only if
there exist a positive integer n and prime ideals Pi(1 ≤ i ≤ n) such that P1∩...∩Pn=0 and the prime ring
R/Pi is right essentially compressible for each 1 ≤ i ≤ n. It follows that a ring R is semiprime right Goldie if and
only if R is a right essentially compressible ring with at least
one uniform right ideal.
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