, for each FP-injective R-module E and for each pure submodule U of finite Goldie dimension of E, E/U is FP-injective
, for each injective R-module E and for each pure submodule U of finite Goldie dimension of E, E/U is injective
, Proof. By Corollary, vol.28, issue.3
, We may assume that E is injective of finite Goldie dimension. By [7, Corollary 28 (E/U ) P is FP-injective
For k = 1, . . . , n, let P k be the maximal ideal of R which verifies that E k is a module over R P k . If S = R \ (P 1 ? · · · ? P n ), then E and U are modules over S ?1 R. So, we replace R with S ?1 R and we assume that R is semilocal. By [12, Theorem 5] each ideal of R is principal (R is Bézout), We have E = E 1 ,
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