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Injective modules over twisted polynomial rings

Published online by Cambridge University Press:  22 January 2016

Barbara L. Osofsky
Barbara L. Osofsky*
Affiliation:
Department of Mathematics Rutgers University, New Brunswick, NJ 08903, U.S.A.
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Differential polynomial rings over a universal field and localized twisted polynomial rings over a separably closed field of non-zero characteristic twisted by the Frobenius endomorphism were the first domains not divisions rings that were shown to have every simple module injective (see [C] and [C-J]). By modifying the separably closed condition for the polynomial rings twisted by the Frobenius, the conditions of every simple being injective and only a single isomorphism class of simple modules were shown to be independent (see [O]). In this paper we continue the investigation of injective cyclic modules over twisted polynomial rings with coefficients in a commutative field.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 119 , September 1990 , pp. 107 - 114
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[C] Cozzens, J. H., Homological properties of the ring: of differential polynomials, Bull. Amer. Math. Soc., 76 (1970), 75–79.CrossRefGoogle Scholar
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[J] Jacobson, N., “The theory of rings,” American Mathematical Soc., Providence, 1943.Google Scholar
[O] Osofsky, B. L., On twisted polynomial rings, J. Algebra, 4 (1971), 597–607.Google Scholar
[O-S] Osofsky, B. L. and Smith, P. F., Cyclic modules whose quotients have complements direct summands, J. Algebra, to appear.Google Scholar
[R] Rotman, J. J., “An introduction to homological algebra,” Academic Press, Inc., Orlando San Diego, 1979.Google Scholar