Abstract
Let R be an associative ring with an identity and (S, ≤) a strictly totally ordered monoid, which is also artinian and finitely generated. If R is left noetherian and M is a left R-module, then we show that i.dim[[R S, ≤]]([M S, ≤]) ≤ i.dim R M. In particular, R M is injective if and only if [[R S, ≤]][M S, ≤] is injective.
ACKNOWLEDGMENTS
Research supported by Foundation for University Key Teacher by the Ministry of Education.