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Modules Over Hereditary Noetherian Prime Rings

Published online by Cambridge University Press:  20 November 2018

Surjeet Singh
Surjeet Singh*
Affiliation:
Ohio University, Athens, Ohio; Guru Nanak University, Amritsar, India
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Quasi-injective and quasi-projective modules over hereditary noetherian prime rings ((hnp)-rings) were studied in [17]. In the present paper we give some applications of the results established in [17]. Kulikov, Kertesz, Prufer, Szele had made basic contributions to the problem of decomposability of abelian p-groups (Fuchs [4]). Kaplansky [9] studied analogous problems for modules over (commutative) Dedekind domains. Let R be an (hnp)-r'mg, which is not right primitive. Using the structure of an indecomposable infective torsion R-module, established in [17, Theorem 4], some of the basic concepts and results on the decomposability of a torsion abelian group are generalized in Section 2, to modules over R.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 4 , 01 August 1975 , pp. 867 - 883
Copyright
Copyright © Canadian Mathematical Society 1975

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