It is not true in general, that localization preserves injectivity. It is shown that if a regular injective R-module, E. is localized at a maximal ideal M, then E sub M is an S-injective R sub M module (where S is the image of the regular elements in R sub M provided that R is h-local. The converse is also true, i.e., if E sub M is S-injective for all maximal ideals M, then E is regular injective. If, in addition, R is an order in a semi-simple ring, then E is an injective R module if and only if E sub M is an injective R sub M-module. If E is regular torsion-free the condition that R must be h-local is redundant.
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