• 1
  • 1
  • 2
  • 6
  • 5
  • 6
  • 3
  • 4
IPM
30
YEARS OLD

“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

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
  Abstract:
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.

Download TeX format
back to top
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
scroll left or right