INJECTIVITY OF MODULES OF GENERALIZED INVERSE POLYNOMIALS

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.

Keywords:

• Generalized power series
• Generalized inverse polynomials
• Strictly totally ordered monoid

ACKNOWLEDGMENTS

Research supported by Foundation for University Key Teacher by the Ministry of Education.