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- W2247456961 abstract "Let $R$ be a ring, and $n$ a fixed nonnegative integer. An $R$-module $W$ is called $L_{n}$-injective if ${rm Ext}_{R}^{1}(M,W)=0$ for any $R$-module $M$ with flat dimension at most $n$. In this paper, we prove first that ($mathcal{F}_{n},mathcal{L}_{n}$) is a complete hereditary cotorsion theory, where $mathcal{F}_n$ (resp. $mathcal{L}_n$) denotes the class of all $R$-modules with flat dimension at most $n$ (resp. $L_{n}$-injective $R$-modules). Then we introduce the $L_{n}$-injective dimension of a module and $L_n$-global dimension of a ring. Finally, over rings with weak global dimension $leq n$, perfect rings, and $L_n$-hereditary rings, more properties and applications of $L_{n}$-injective modules, $L_{n}$-injective dimensions of modules and $mathcal{L}_{n}$-global dimensions of rings are given." @default.
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- W2247456961 date "2015-09-24" @default.
- W2247456961 modified "2023-09-27" @default.
- W2247456961 title "On $L_{n}$-Injective Modules and $L_{n}$-Injective Dimensions" @default.
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