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Morita Context and Morita-Like Equivalence for the xst-Rings

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Abstract

The notion of the xst-rings was introduced by García and Marín [5] in 1999. In this paper, we consider Morita context, Morita-like equivalence and the exchange property for the xst-rings. The results of the first Morita theorem are generalized to the xst-rings. So we obtain an important Morita-like equivalence of the xst-rings, from which, as an immediate consequence, we deduce the main result of Xu-Shum-Turner [4] and the standard Morita equivalence, A ∼ M n (A), for a unital ring A. Moreover, we describe the properties of those well-known intermediate matrix rings, and show that the exchange property of a unital ring A coincides with the one for any M n (A) as well as any intermediate matrix ring sitting between FM Γ(A) and FC Γ(A), which is an extension of a well-known result obtained by Nicholson [7].

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Authors and Affiliations

  1. Department of Mathematics, Hunan Normal University, Changsha 410081, P. R. China

    Bai Yu Ouyang

  2. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

    Bai Yu Ouyang

  3. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

    Wen Ting Tong

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  1. Bai Yu Ouyang
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  2. Wen Ting Tong
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Correspondence to Bai Yu Ouyang.

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Partially supported by the National Science Foundation of China (10071035)

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Ouyang, B.Y., Tong, W.T. Morita Context and Morita-Like Equivalence for the xst-Rings. Acta Math Sinica 19, 371–380 (2003). https://doi.org/10.1007/s10114-002-0219-1

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  • DOI: https://doi.org/10.1007/s10114-002-0219-1

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