Geodesic
Rings which have $(m,n)$-flat injective modules
Algebra and discrete mathematics, no. 4 (2005), pp. 93-100

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A ring $R$ is said to be a left $IF-(m,n)$ ring if every injective left $R$-module is $(m,n)$-flat. In this paper, several characterizations of left $IF-(m,n)$ rings are investigated, some conditions under which $R$ is left $IF-(m,n)$ are given. Furthermore, conditions under which a left $IF-1$ ring (i.e., $IF-(1,1)$ ring) is a field, a regular ring and a semisimple ring are studied respectively.
Keywords: injective modules; $(m,n)$-flat modules; left $IF-(m,n)$ rings; left $IF-1$ rings. 
@article{ADM_2005_4_a6,
     author = {Zh. Zhanmin and X. Zhangsheng},
     title = {Rings which have $(m,n)$-flat injective modules},
     journal = {Algebra and discrete mathematics},
     pages = {93--100},
     publisher = {mathdoc},
     number = {4},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2005_4_a6/}
}
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Zh. Zhanmin; X. Zhangsheng. Rings which have $(m,n)$-flat injective modules. Algebra and discrete mathematics, no. 4 (2005), pp. 93-100. http://geodesic.mathdoc.fr/item/ADM_2005_4_a6/