DOI QR코드

DOI QR Code

COMULTIPLICATION MODULES AND RELATED RESULTS

  • Ansari-Toroghy, H. (Department of Mathematics, Faculty of Science, Guilan University) ;
  • Farshadifar, F. (Department of Mathematics, Faculty of Science, Guilan University)
  • Received : 2007.10.25
  • Accepted : 2008.01.10
  • Published : 2008.03.25

Abstract

Let R be a commutative ring (with identity). In this paper we will obtain some results concerning comultiplication R-modules. Further we state and prove a dual notion of Nakayama's lemma for finitely cogenerated modules.

References

  1. W. Anderson and K.R. Fuller, Rings and categories of modules, Springer-Verlag, New York-Heidelberg-Berlin, 1974.
  2. H. Ansari-Toroghy, Associated and coassociated primes, Communication in Algebra, (2) 26 (1998), 453-466. https://doi.org/10.1080/00927879808826141
  3. H. Ansari-Toroghy and F. Farshadifar, The dual notion of multiplication modules, Taiwanese Journal of Mathematics, (4) 11 (2007), 1189-1201. https://doi.org/10.11650/twjm/1500404812
  4. H. Ansari-Toroghy and F. Farshadifar, On comultiplication modules, submitted.
  5. C.M. Low and P.F .Smith, Multiplication modules and ideals, Comm. Algebra, (18) 12 (1990), 4353-4375.
  6. D.W. Sharpe and P. Vamos, Injective modules, Cambridge university Press, London 1972.

Cited by

  1. On multiplication and comultiplication modules vol.31, pp.2, 2011, https://doi.org/10.1016/S0252-9602(11)60269-5
  2. On the Dual Notion of Multiplication Modules vol.36, pp.6, 2011, https://doi.org/10.1007/s13369-011-0088-y
  3. Comultiplication Modules over Noncommutative Rings vol.191, pp.5, 2013, https://doi.org/10.1007/s10958-013-1357-y
  4. The Dual Notion of Content Modules vol.44, pp.11, 2016, https://doi.org/10.1080/00927872.2015.1110587
  5. Модули, у которых все подмодули являются аннуляторами vol.24, pp.3, 2012, https://doi.org/10.4213/dm1195
  6. On the Dual Notion of Prime Submodules (II) vol.9, pp.2, 2012, https://doi.org/10.1007/s00009-011-0129-5