In:
Mathematica Slovaca, Walter de Gruyter GmbH, Vol. 57, No. 4 ( 2007-8-1), p. 333-338
Abstract:
In this note we are going to show that if M is a left module over a left noetherian ring R of the infinite cardinality λ ≥ |R|, then its injective hull E(M) is of the same size. Further, if M is an injective module with |M| ≥ (2λ)+ and K ≤ M is its submodule such that |M/K| ≤ λ, then K contains an injective submodule L with |M/L| ≤ 2λ. These results are applied to modules which are torsionfree with respect to a given hereditary torsion theory and generalize the results obtained by different methods in author’s previous papers: [A note on pure subgroups, Contributions to General Algebra 12. Proceedings of the Vienna Conference, June 3–6, 1999, Verlag Johannes Heyn, Klagenfurt, 2000, pp. 105–107], [Pure subgroups, Math. Bohem. 126 (2001), 649–652] .
Type of Medium:
Online Resource
ISSN:
1337-2211
,
0139-9918
DOI:
10.2478/s12175-007-0027-2
Language:
English
Publisher:
Walter de Gruyter GmbH
Publication Date:
2007
detail.hit.zdb_id:
2393408-6
SSG:
17,1
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