Skip to main content

Isomorphism classes and adjoints of certain iwasawa modules


Letp be an odd prime number andO the integer ring of a finite extension of ℚ p . We determine isomorphism classes of certainO[[T]]-modules which are isomorphic toO ⊕3 asO-modules. Moreover we give some examples which are not isomorphic to their adjoints.

This is a preview of subscription content, access via your institution.


  1. [1]

    L. Federer, Noetherian ℤ p [[T]]-modules, adjoints, and Iwasawa theory.Illinois J. Math. 30 (1986), 636–652.

    MATH  MathSciNet  Google Scholar 

  2. [2]

    K. Iwasawa, On ℤ ℤl-extensions of algebraic number fields.Ann. of Math. 98 (1973), 246–326.

    Article  MathSciNet  Google Scholar 

  3. [3]

    M. Koike, On the isomorphism classes of Iwasawa modules associated to imaginary quadratic fields with λ = 2.J. Math. Sci. Univ. Tokyo 6 (1999), 371–396.

    MATH  MathSciNet  Google Scholar 

  4. [4]

    H. Sumida, Greenberg’s conjecture and the Iwasawa polynomial.J. Math. Soc. Japan 49 (1997), 689–711.

    MATH  MathSciNet  Article  Google Scholar 

  5. [5]

    L. Washington,Introduction to Cyclotomic Fields. 2nd ed. Springer, 1997.

Download references

Author information



Corresponding author

Correspondence to Hiroki Sumida.

Additional information

Partly supported by the Grants-in-Aid for Encouragement of Young Scientists (No. 11740020), The Ministry of Education, Science, Sports and Culture of Japan.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sumida, H. Isomorphism classes and adjoints of certain iwasawa modules. Abh.Math.Semin.Univ.Hambg. 70, 113 (2000).

Download citation

Key words and phrases

  • Iwasawa module
  • adjoints
  • Λ-isomorphism