标题： 极小内射模为内射环的研究 显示英文标题

标题： Rings whose mininjective modules are injective

摘要： 本文的主要目的是刻画使得极小内射模为内射模的环，从而使极小内射模类与内射模类重合。 我们证明这些环恰好是满足每个极小平坦模都是投射模的诺特环，并且在环为Kasch环、交换环以及拟Frobenius环时研究了这一刻画。 我们也处理了上三角矩阵环 $n\times n$ 的情况，证明其极小内射模为内射模当且仅当 $n=2$。 我们利用已发展的工具找到了一类新的贫子内射模（其子内射域仅包含内射模）的例子，到目前为止，这类模的存在性仅在某些相当受限的情况下被发现。 显示英文摘要

摘要： The main goal of this paper is to characterize rings over which the mininjective modules are injective, so that the classes of mininjective modules and injective modules coincide. We show that these rings are precisely those Noetherian rings for which every min-flat module is projective and we study this characterization in the cases when the ring is Kasch, commutative and when it is quasi-Frobenius. We also treat the case of $n\times n$ upper triangular matrix rings, proving that their mininjective modules are injective if and only if $n=2$. We use the developed machinery to find a new type of examples of indigent modules (those whose subinjectivity domain contains only the injective modules), whose existence is known, so far, only in some rather restricted situations.