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A Note on Skolem-Noether Algebras

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Abstract

The paper was motivated by Kovacs’ paper (1973), Isaacs’ paper (1980) and a recent paper, due to Bresar et al. (2018), concerning Skolem-Noether algebras. Let K be a unital commutative ring, not necessarily a field. Given a unital K-algebra S, where K is contained in the center of S, n ∈ ℕ, the goal of this paper is to study the question: when can a homomorphism ϕ: Mn(K) → Mn(S) be extended to an inner automorphism of Mn(S)? As an application of main results presented in the paper, it is proved that if S is a semilocal algebra with a central separable subalgebra R, then any homomorphism from R into S can be extended to an inner automorphism of S.

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Acknowledgments

The authors would like to express their thanks to the referee for valuable suggestions and careful reading.

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Authors and Affiliations

  1. Department of Mathematics Education, Pusan National University, 2, Busandaehak-ro 63beon-gil, Geumjeong-gu, Pusan, 609-735, South Korea

    Juncheol Han

  2. Department of Mathematics, National Taiwan University, Astronomy Mathematics Building 5F, No. 1, Sec. 4, Roosevelt Rd., Taipei, 10617, Taiwan

    Tsiu-Kwen Lee

  3. Department of Mathematics, Dong-A University, 37 Nakdong-daero 550beon-gil Saha-gu, Pusan, 604-714, South Korea

    Sangwon Park

Authors
  1. Juncheol Han
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  2. Tsiu-Kwen Lee
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  3. Sangwon Park
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Corresponding author

Correspondence to Tsiu-Kwen Lee.

Additional information

The work of T.-K. Lee was supported in part by the Ministry of Science and Technology of Taiwan (MOST 107-2115-M-002-018-MY2) and the NCTS (Taipei Office).

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Han, J., Lee, TK. & Park, S. A Note on Skolem-Noether Algebras. Czech Math J 71, 137–154 (2021). https://doi.org/10.21136/CMJ.2020.0215-19

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  • DOI: https://doi.org/10.21136/CMJ.2020.0215-19

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