Advanced search
Publication Cover
Communications in Algebra Volume 41, 2013 - Issue 1
Submit an article Journal homepage
320
Views
21
CrossRef citations to date
0
Altmetric
Original Articles

Second Modules Over Noncommutative Rings

S. Çeken Department of Mathematics, Akdeniz University, Antalya, Turkey
,
M. Alkan Department of Mathematics, Akdeniz University, Antalya, Turkey; Department of Mathematics, University of Glasgow, Glasgow, Scotland, UKCorrespondence[email protected]
&
P. F. Smith Department of Mathematics, University of Glasgow, Glasgow, Scotland, UK
Pages 83-98 | Received 09 Feb 2011, Published online: 04 Jan 2013

REFERENCES

  • Abuhlail , J. Zariski topologies for coprime and second submodules. Algebra Colloquium, to appear.
  • Alkan , M. , Tiras , Y. ( 2007 ). On prime submodules . Rocky. Moun. J. Math. 37 : 709 – 722 .
  • Alkan , M. , Tiras , Y. ( 2006 ). Projective modules and prime submodules . Czech. Math. J. 56 ( 2 ): 601 – 611 .
  • Anderson , F. W. , Fuller , K. R. ( 1974 ). Rings and Categories of Modules . New York : Springer-Verlag .
  • Annin , S. ( 2008 ). Attached primes over noncommutative rings . J. Pure Appl. Algebra 212 : 510 – 521 .
  • Ansari-Toroghy , H. , Farshadifar , F. On the dual notion of prime submodules. Algebra Coll., to appear.
  • Ansari-Toroghy , H. Farshadifar , F. ( 2011 ). The dual notions of some generalizations of prime submodules . Comm. Algebra 39 : 2396 – 2416 .
  • Clark , J. , Lomp , C. , Vanaja , N. , Wisbauer , R. ( 2006 ). Lifting Modules . Basel : Birkhäuser Verlag .
  • Dauns , J. ( 1978 ). Prime modules . J. Reine Angew Math. 298 : 156 – 181 .
  • Dauns , J. ( 1980 ). Prime modules and one-sided ideals, in Ring Theory and Algebra III, Proceedings of the Third Oklahoma Conference (B. R. McDonald, ed.) Dekker, New York, pp. 301–344 .
  • Ebrahimi-Atani , S. ( 2001 ). On secondary modules over Dedekind domains . Southeast Asian Bull. Math. 25 ( 1 ): 1 – 6 .
  • Ebrahimi-Atani , S. ( 2002 ). Submodules of secondary modules . Int. J. Math. Math. Sci. 31 : 321 – 327 .
  • Levy , L. ( 1963 ). Torsion-free and divisible modules over non-integral domains . Canad. J. Math. 15 : 132 – 151 .
  • Lu , C.-P. ( 1984 ). Prime submodules of modules. Comm. Math. Univ. Sancti Pauli 33: 61–69 .
  • Lu , C.-P. ( 1989 ). M-radicals of submodule of modules . Math. Japon. 34 : 211 – 219 .
  • McCasland , R. L. , Moore , M. E. (1992). Prime submodules. Comm. Algebra 20: 1803–1817.
  • McCasland , R. L. , Smith , P. F. ( 1993 ). Prime submodules of Noetherian modules . Rocky Mtn. J. 23 : 1041 – 1062 .
  • McConnell , J. C. , Robson , J. C. ( 1987 ). Noncommutative Noetherian Rings . Chichester : Wiley-Interscience .
  • Nicholson , W. K. , Yousif , M. F. ( 2003 ). Quasi-Frobenius Rings . Cambridge Tracts in Mathematics . Vol. 158 . Cambridge : Cambridge Univ. Press .
  • Sharpe , D. W. , Vamos , P. ( 1972 ). Injective Modules . Cambridge Tracts in Mathematics . Vol. 62 . Cambridge : Cambridge Univ. Press .
  • Smith , P. F. ( 1981 ). Injective modules and prime ideals . Comm. Algebra 9 : 989 – 999 .
  • Tiras , Y. , Harmanci , A. , Smith , P. F. ( 1999 ). A characterization of prime submodules . J. Algebra 212 : 743 – 752 .
  • Yassemi , S. ( 2001 ). The dual notion of prime submodules. Arch. Math. Brno. 37: 273–278 .
  • Communicated by T. Albu.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.