Geodesic
Extensions that are Submodules of their Quotients
Canadian mathematical bulletin, Tome 33 (1990) no. 1, pp. 93-99

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Let 0 → N → E → F → 0 be a short exact sequence of torsion-free Kronecker modules. Suppose that N and F have rank one. The module F is classified by a height function h defined on the projective line. If N is finite-dimensional, h is supported on a set of cardinality less than that of its domain and h takes on the value ∞, then E embeds into F. The converse holds if all such E embed into F. This embeddability is in contrast to the situation with other rings such as commutative domains, where it never occurs.
DOI : 10.4153/CMB-1990-016-0
Mots-clés : 16A64, 16A46 
Okoh, F.; Zorzitto, F. Extensions that are Submodules of their Quotients. Canadian mathematical bulletin, Tome 33 (1990) no. 1, pp. 93-99. doi: 10.4153/CMB-1990-016-0
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     title = {Extensions that are {Submodules} of their {Quotients}},
     journal = {Canadian mathematical bulletin},
     pages = {93--99},
     year = {1990},
     volume = {33},
     number = {1},
     doi = {10.4153/CMB-1990-016-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-016-0/}
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