Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-30T21:36:39.509Z Has data issue: false hasContentIssue false

Modules Behaving Like Torsion Abelian Groups

Published online by Cambridge University Press:  20 November 2018

M. Zubair Khan*
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh-202001, India
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Recently H. Marubayashi [1,2] and S. Singh [10,11,12] generalized some results of torsion abelian groups for modules over some restricted rings, like bounded Dedekind prime rings, bounded hereditary Noetherian prime rings. Singh [12] introduced the concept of h-purity for a module MR satisfying the following conditions:

(I) Every finitely generated submodule of every homomorphic image of M is a direct sum of uniserial modules.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1979

References

1,2. Marubayashi, H., Modules over bounded dedekind prime rings, I, II, Osaka J. Math. 9(1872), 95-110, 427-445.Google Scholar
3. Irwin, J. M., High subgroups of abelian torsion groups, Pacific J. Math. 11 (1961).Google Scholar
4. Irwin, J. M. and Walker, E. A., On N-high subgroups of abelian groups, Pacific J. Math. 11 (1961), 1363-1374.Google Scholar
5. Fuchs, L., Infinite abelian groups, Vol. I, Academic press, New York (1970).Google Scholar
6. Fuchs, L., Infinite abelian groups, Vol. II, Academic Press, New York (1973).Google Scholar
7. Khan, Musharafuddin, Torsion modules over bounded (hnp)rings Ph-D. Dissertation (1976).Google Scholar
8. Zubair Khan, M., Modules behaving like torsion abelian groups (Abstract), Notices Amer. Math. Soc. June (1977).Google Scholar
9. Hill, P., Certain pure subgroups of primary groups; Topics in abelian groups, Scott Foresman and Co. (1963).Google Scholar
10,11. Singh, S., Modules over (hnp)-rings, I, II; Canadian J. Math. 27 (1975) 867-883, Canadian J. Math 28 (1976), 73–82.Google Scholar
12. Singh, S., Some decomposition theorems in abelian groups and their generalizations; Ring theory, Proc. of Ohio Univ. Conference Marcel Dekker, N.Y. (1976), 183-189.Google Scholar