Equivalent Presentations of Modules Over Prüfer Domains
Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 151-157

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If $F$ and ${F}'$ are free $R$ -modules, then $M\cong F/H$ and $M\,\cong \,{F}'\,/\,{H}'$ are viewed as equivalent presentations of the $R$ -module $M$ if there is an isomorphism $F\,\to \,{F}'$ which carries the submodule $H$ onto ${H}'$ . We study when presentations of modules of projective dimension 1 over Prüfer domains of finite character are necessarily equivalent.
DOI : 10.4153/CMB-1998-024-6
Mots-clés : 13C11
Fuchs, Laszlo; Lee, Sang Bum. Equivalent Presentations of Modules Over Prüfer Domains. Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 151-157. doi: 10.4153/CMB-1998-024-6
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[1] 1. Brewer, J. and Klingler, L., Pole assignability and the invariant factor theorem in Prüfer domains and Dedekind domains. J.Algebra 114 (1987), 536–545. Google Scholar

[2] 2. Cohen, J. and Gluck, H., Stacked bases for modules over principal ideal domains. J. Algebra 14 (1970), 493–505. Google Scholar

[3] 3. Erdőos, J., Torsion-free factor groups of free abelian groups and a classification of torsion-free abelian groups. Publ. Math. Debrecen 5 (1957), 172–184. Google Scholar

[4] 4. Fuchs, L., Abelian Groups. Akadémiai Kiadó, Budapest, 1958. Google Scholar

[5] 5. Fuchs, L., Note on modules of projective dimension one. In: Abelian Group Theory, Gordon and Breach Science Publishers, New York etc., 1986. Google Scholar

[6] 6. Heitmann, R. C. and Levy, L. S., 1 1/2 and 2 generator ideals in Prüfer domains. RockyMountain J. Math. 5 (1975), 361–373. Google Scholar

[7] 7. Hill, P. and Megibben, C., Generalizations of the stacked bases theorem. Trans.Amer.Math. Soc. 312 (1989), 377–402. Google Scholar

[8] 8. Kaplansky, I., Modules over Dedekind rings and valuation rings. Trans. Amer.Math. Soc. 72(1952), 327–340. Google Scholar

[9] 9. Levy, L. S., Invariant factor theorem for Prüfer domains of finite character. J. Algebra 106 (1987), 259–264. Google Scholar

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