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Paper   IPM / M / 8001
School of Mathematics
  Title:   Essentially compressible modules and rings
  Author(s):  M. R. Vedadi (Joint with P. F. Smith)
  Status:   Published
  Journal: J. Algebra
  Vol.:  304
  Year:  2006
  Pages:   812-831
  Supported by:  IPM
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 ≤ in) such that P1∩...∩Pn=0 and the prime ring R/Pi is right essentially compressible for each 1 ≤ in. 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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