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On extensions of matrix rings with skew Hochschild 2-cocycles

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Abstract

We study structures of Hochschild 2-cocycles related to endomorphisms and introduce a skew Hochschild 2-cocycle. We moreover define skew Hochschild extensions equipped with skew Hochschild 2-cocycles, and then we examine uniquely clean, Abelian, directly finite, symmetric, and reversible ring properties of skew Hochschild extensions and related ring systems. The results obtained here provide various kinds of examples of such rings. Especially, we give an answer negatively to the question of H. Lin and C. Xi for the corresponding Hochschild extensions of reversible (or semicommutative) rings. Finally, we establish three kinds of Hochschild extensions with Hochschild 2-cocycles and skew Hochschild 2-cocycles.

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Authors and Affiliations

  1. Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul, 02447, Korea

    Chan Yong Hong

  2. School of Basic Sciences, Hanbat National University, Daejeon, 34158, Korea

    Nam Kyun Kim

  3. Department of Mathematics, Daejin University, Pocheon, 11159, Korea

    Tai Keun Kwak

  4. Department of Mathematics, Pusan National University, Pusan, 46241, Korea

    Yang Lee

Authors
  1. Chan Yong Hong
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  2. Nam Kyun Kim
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  3. Tai Keun Kwak
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  4. Yang Lee
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Correspondence to Nam Kyun Kim.

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Hong, C.Y., Kim, N.K., Kwak, T.K. et al. On extensions of matrix rings with skew Hochschild 2-cocycles. Front. Math. China 11, 869–900 (2016). https://doi.org/10.1007/s11464-016-0552-9

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  • DOI: https://doi.org/10.1007/s11464-016-0552-9

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