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A Note on Annihilator Relations
Published online by Cambridge University Press: 22 January 2016
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In a Frobenius algebra A over a field K, there exists a linear function λ of A into K which does not map any proper ideal of A onto 0. Then the map φ : x → xφ where
λ(xy) = λ(yxφ) for all y ε A,
defines an automorphism φ of A onto itself. This automorphism is called Nakayama’s automorphism. Now the following result is well known.
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- Research Article
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1960
References
1) T. Nakayama, On Frobeniusean algebras II, Ann. of Math., 42 (1941), pp. 1-21.
2) This formulation of theorem is due to T. Nakayama. The writer’s original theorem was more special.
3) This theorem is valid if A is a semi-group with zero.
4) It is well known that this relation holds in a quasi-Frobenius rin.
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