Stability, duality, 2-generated ideals and a canonical decomposition of modules
Rendiconti del Seminario Matematico della Università di Padova, Tome 106 (2001), pp. 261-290.
@article{RSMUP_2001__106__261_0,
     author = {Olberding, Bruce},
     title = {Stability, duality, $2$-generated ideals and a canonical decomposition of modules},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {261--290},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {106},
     year = {2001},
     mrnumber = {1876223},
     zbl = {1072.13506},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_2001__106__261_0/}
}
TY  - JOUR
AU  - Olberding, Bruce
TI  - Stability, duality, $2$-generated ideals and a canonical decomposition of modules
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2001
SP  - 261
EP  - 290
VL  - 106
PB  - Seminario Matematico of the University of Padua
UR  - http://archive.numdam.org/item/RSMUP_2001__106__261_0/
LA  - en
ID  - RSMUP_2001__106__261_0
ER  - 
%0 Journal Article
%A Olberding, Bruce
%T Stability, duality, $2$-generated ideals and a canonical decomposition of modules
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2001
%P 261-290
%V 106
%I Seminario Matematico of the University of Padua
%U http://archive.numdam.org/item/RSMUP_2001__106__261_0/
%G en
%F RSMUP_2001__106__261_0
Olberding, Bruce. Stability, duality, $2$-generated ideals and a canonical decomposition of modules. Rendiconti del Seminario Matematico della Università di Padova, Tome 106 (2001), pp. 261-290. http://archive.numdam.org/item/RSMUP_2001__106__261_0/

[1] H. Bass, On the ubiquity of Gorenstein rings, Math. Z., 82 (1963), pp. 8-28. | MR | Zbl

[2] S. Bazzoni - L. Salce, Warfield domains, J. of Alg., 185 (1996), pp. 836-868. | MR | Zbl

[3] Z.I. Borevic - D.K. Fadeev, Representations of orders with a cyclic index, Trudy Mat. Inst. Steklov, 80 (1965), pp. 51-65 (in Russian); English Translation: Proc. Steklov. Inst. Math., 80 (1965), pp. 56-72. | MR | Zbl

[4] W. Brandal, Almost maximal integral domains and finitely generated modules, Trans. Amer. Math. Soc., 183 (1973), pp. 203-222. | MR | Zbl

[5] D. Eisenbud - W. VASCONCELOS - R. WIEGAND, Projective summands in generators, Nagoya Math. J., 80 (1982), pp. 203-209. | MR | Zbl

[6] A. Facchini, Generalized Dedekind domains and their injective modules, J. Pure and Appl. Algebra, 94 (1994), pp. 159-173. | MR | Zbl

[7] M. Fontana - J. Huckaba - I. Papick, Prüfer Domains, Marcel Dekker, New York, 1997. | MR | Zbl

[8] W. Heinzer, Integral domains in which every non-zero ideal is divisorial, Mathematika, 15 (1968), pp. 164-169. | MR | Zbl

[9] L. Levy - R. Wiegand, Dedekind-like behavior of rings with 2-generated ideals, J. Pure and Appl. Algebra, 37 (1985), pp. 41-58. | MR | Zbl

[10] J. Lipman, Stable ideals and Arf rings, Amer. J. Math., 93 (1971), pp. 649-685. | MR | Zbl

[11] E. Matlis, Torsion-free modules, The University of Chicago Press, Chicago, 1972. | MR | Zbl

[12] E. Matlis, Injective modules over Prüfer domains, Nagoya Math. J., 15 (1959), pp. 57-69. | MR | Zbl

[13] B. Olberding, Almost maximal Prüfer domains, Comm. in Alg., 27 (1999), pp. 4433-4458. | MR | Zbl

[14] B. Olberding, On the classification of stable domains, J. Algebra, in press. | MR | Zbl

[15] B. Olberding, Factorization into prime and invertible ideals, J. London Math. Soc., 62 (2000), pp. 336-344. | MR | Zbl

[16] B. Olberding, Globalizing local properties of Prüfer domains, J. Algebra., 205 (1998), pp. 480-504. | MR | Zbl

[17] B. Olberding, Modules of injective dimension one over Prüfer domains, J. Pure Appl. Algebra, 153 (2000), pp. 263-287. | MR | Zbl

[18] B. Olberding, On the structure of stable domains, Comm. Algebra, to appear. | MR | Zbl

[19] D. Rush, 2-generated ideals and representations of abelian groups over valuation rings, J. of Alg., 177 (1995), pp. 77-101. | MR | Zbl

[20] D. Rush, Rings with 2-generated ideals, J. Pure Appl. Alg., 73 (1991), pp. 257-275. | MR | Zbl

[21] J.D. Sally - W.V. Vasconcelos, Stable rings, J. Pure Appl. Alg., 4 (1974), pp. 319-336. | MR | Zbl

[22] J.D. Sally and W.V. Vasconcelos, Stable rings and a problem of Bass, Bull. Am. Math. Soc., 79 (1973), pp. 575-576. | MR | Zbl

[23] R.B. Warfieldjr., Cancellation of modules and groups and stable range of endomorphism rings, Pacific J. Math., 91 (1980), pp. 457-485. | MR | Zbl