The S-transform and its dual with applications to Prüfer extensions
Rendiconti del Seminario Matematico della Università di Padova, Tome 95 (1996), pp. 201-216.
@article{RSMUP_1996__95__201_0,
     author = {Rhodes, Christopher P. L.},
     title = {The $S$-transform and its dual with applications to {Pr\"ufer} extensions},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {201--216},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {95},
     year = {1996},
     mrnumber = {1405364},
     zbl = {0880.13002},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1996__95__201_0/}
}
TY  - JOUR
AU  - Rhodes, Christopher P. L.
TI  - The $S$-transform and its dual with applications to Prüfer extensions
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 1996
SP  - 201
EP  - 216
VL  - 95
PB  - Seminario Matematico of the University of Padua
UR  - http://www.numdam.org/item/RSMUP_1996__95__201_0/
LA  - en
ID  - RSMUP_1996__95__201_0
ER  - 
%0 Journal Article
%A Rhodes, Christopher P. L.
%T The $S$-transform and its dual with applications to Prüfer extensions
%J Rendiconti del Seminario Matematico della Università di Padova
%D 1996
%P 201-216
%V 95
%I Seminario Matematico of the University of Padua
%U http://www.numdam.org/item/RSMUP_1996__95__201_0/
%G en
%F RSMUP_1996__95__201_0
Rhodes, Christopher P. L. The $S$-transform and its dual with applications to Prüfer extensions. Rendiconti del Seminario Matematico della Università di Padova, Tome 95 (1996), pp. 201-216. http://www.numdam.org/item/RSMUP_1996__95__201_0/

[1] D.F. Anderson - A. Bouvier, Ideal transforms, and overrings of a quasilocal integral domain, Ann. Univ. Ferrara, 32 (1986), pp. 15-38. | MR | Zbl

[2] J.T. Arnold - J.W. Brewer, On flat overrings, ideal transforms and generalized transforms of a commutative ring, J. Algebra, 18 (1971), pp. 254-263. | MR | Zbl

[3] J.W. Brewer, The ideal transform and overrings of an integral domain, Math. Z., 107 (1968), pp. 301-306. | MR | Zbl

[4] R.W. Gilmer, Overrings of Prüfer domains, J. Algebra, 4 (1966), pp. 331-340. | MR | Zbl

[5] R.W. Gilmer, Multiplicative Ideal Theory, Marcel Dekker, New York and Basel (1972). | MR | Zbl

[6] R.W. Gilmer - W.J. Heinzer, Overrings of Prüfer domains. II, J. Algebra, 7 (1967), pp. 281-302. | MR | Zbl

[7] M. Griffin, Prüfer rings with zero divisors, J. Reine Angew. Math., 239-240 (1969), pp. 55-67. | MR | Zbl

[8] M. Griffin, Valuations and Prüfer rings, Can. J. Math., 26 (1974), pp. 412-429. | MR | Zbl

[9] J.H. Hays, The S-transform and the ideal transform, J. Algebra, 57 (1979), pp. 223-229. | MR | Zbl

[10] W.J. Heinzer - J. Ohm - R.L. Pendleton, On integral domains of the form ∩ Dp, P minimal, J. Reine Angew. Math., 241 (1970), pp. 147-159. | EuDML | MR | Zbl

[11] J.A. Huckaba, Commutative Rings with Zero Divisors, Marcel Dekker, New York and Basel (1988). | MR | Zbl

[12] J.A. Huckaba - I.J. Papick, When the dual of an ideal is a ring, Manuscripta Math., 37 (1982), pp. 67-85. | EuDML | MR | Zbl

[13] I. Kaplansky, Commutative Rings, Polygonal Publishing House, Washington, New Jersey (1994).

[14] R. Matsuda, Generalizations of multiplicative ideal theory to commutative rings with zerodivisors, Bull. Fac. Sci. Ibaraki U., Ser. A Math., 17 (1985), pp. 49-101. | MR | Zbl

[15] M. Nagata, A treatise on the 14-th problem of Hilbert, Mem. Coll. Sci. Univ. Kyoto, 30 (1956), pp. 57-70. | MR | Zbl

[16] M. Nagata, Some sufficient conditions for the fourteenth problem of Hilbert, Actas Del Coloquio Internac. Sobre Geometria Algebraica (1965), pp. 107-121. | MR | Zbl

[17] C.P.L. Rhodes, On valuation subalgebras and their centres, Glasgow Math. J., 31 (1989), pp. 115-126. | MR | Zbl

[18] C.P.L. Rhodes, Relatively Prüfer pairs of commutative rings, Comm. Algebra, 19 (1991), pp. 3423-3445. | MR | Zbl

[19] P. Schenzel, When is a flact algebra of finite type ?, Proc. Amer. Math. Soc., 109 (1990), pp. 287-290. | MR | Zbl