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Text File  |  1992-08-12  |  1.1 KB  |  26 lines
  1. Newsgroups: sci.math
  2. Path: sparky!uunet!snorkelwacker.mit.edu!thunder.mcrcim.mcgill.edu!triples.math.mcgill.ca!boshuck
  3. From: boshuck@triples.math.mcgill.ca (William Boshuck)
  4. Subject: Re: The Converse of Kaplansky's Therorem
  5. Message-ID: <1992Aug12.165234.11088@thunder.mcrcim.mcgill.edu>
  6. Sender: news@thunder.mcrcim.mcgill.edu
  7. Nntp-Posting-Host: triples.math.mcgill.ca
  8. Organization: Dept Of Mathematics and Statistics
  9. References: <1349@newsserver.cs.uwindsor.ca>
  10. Date: Wed, 12 Aug 92 16:52:34 GMT
  11. Lines: 14
  12.  
  13. In article <1349@newsserver.cs.uwindsor.ca> tarokh@server.uwindsor.ca (TAROKH VAHID             ) writes:
  14. >Would somebody please tell me if the converse of Kaplansky's Theorem
  15. >is true or not? That is if R is a ring with identity such that all the
  16. >projective R modules are free, then is R necessarily Local? If we assume
  17. >that R does not have identity what could be said?
  18. >
  19. >Thank You,
  20. >Vahid Tarokh
  21. >
  22.  
  23. The answer to the first question is NO. Look at the ring of integers.
  24. I haven't thought about the second question since I have absolutely
  25. no experience with rings without identity.
  26.