Journal of Mathematical Sciences

, Volume 183, Issue 5, pp 675–680 | Cite as

Nakayama functors and Eilenberg-Watts theorems


In the present paper, analogs of the Eilenberg-Watts theorem are proved for categories of finitely generated modules over finite-dimensional algebras for right exact and left exact functors. Furthermore, for left exact functors the corresponding bimodules are described explicitly. The main aim of this paper is to present how, with these versions of the Eilenberg-Watts theorem, we obtain some new descriptions of the Nakayama functor and the inverse Nakayama functor in the case of self-injective algebras. Bibliography: 4 titles.


Exact Functor Left Exact Functor Nakayama Functor 


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  1. 1.
    S. Eilenberg, “Abstract description of some basic functors,” J. Indian Math. Soc., 24, 231–234 (1960).MathSciNetGoogle Scholar
  2. 2.
    C. E. Watts, “Intrinsic characterizations of some additive functors,” Proc. Amer. Math. Soc., 11, 5–8 (1960).MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    I. Assem, D. Simson and A. Skowroński, Elements of Representation Theory of Associative Algebras I: Techniques of Representation Theory, Cambridge Univ. Press, London (2005).Google Scholar
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    M. Auslander, I. Reiten, and S. O. Smalø, Representation Theory of Artin Algebras, Cambridge Univ. Press, London (1995).MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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