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 ...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 ～ Mn(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 Mn(A) as well as any intermediate matrix ring sitting between FM&(A) and FC&(A), which is an extension of a well-known result obtained by Nicholson [7].展开更多
文摘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 ～ Mn(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 Mn(A) as well as any intermediate matrix ring sitting between FM&(A) and FC&(A), which is an extension of a well-known result obtained by Nicholson [7].
