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) , p. 201-216
Zbl 0880.13002 | MR 1405364
URL stable : http://www.numdam.org/item?id=RSMUP_1996__95__201_0

Bibliographie

[1] D.F. Anderson - A. Bouvier, Ideal transforms, and overrings of a quasilocal integral domain, Ann. Univ. Ferrara, 32 (1986), pp. 15-38. MR 901583 | Zbl 0655.13002

[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 276215 | Zbl 0218.13019

[3] J.W. Brewer, The ideal transform and overrings of an integral domain, Math. Z., 107 (1968), pp. 301-306. MR 236158 | Zbl 0167.03601

[4] R.W. Gilmer, Overrings of Prüfer domains, J. Algebra, 4 (1966), pp. 331-340. MR 202749 | Zbl 0146.26205

[5] R.W. Gilmer, Multiplicative Ideal Theory, Marcel Dekker, New York and Basel (1972). MR 427289 | Zbl 0248.13001

[6] R.W. Gilmer - W.J. Heinzer, Overrings of Prüfer domains. II, J. Algebra, 7 (1967), pp. 281-302. MR 217055 | Zbl 0156.04304

[7] M. Griffin, Prüfer rings with zero divisors, J. Reine Angew. Math., 239-240 (1969), pp. 55-67. MR 255527 | Zbl 0185.09801

[8] M. Griffin, Valuations and Prüfer rings, Can. J. Math., 26 (1974), pp. 412-429. MR 345957 | Zbl 0259.13008

[9] J.H. Hays, The S-transform and the ideal transform, J. Algebra, 57 (1979), pp. 223-229. MR 533111 | Zbl 0427.13007

[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. Zbl 0191.32202

[11] J.A. Huckaba, Commutative Rings with Zero Divisors, Marcel Dekker, New York and Basel (1988). MR 938741 | Zbl 0637.13001

[12] J.A. Huckaba - I.J. Papick, When the dual of an ideal is a ring, Manuscripta Math., 37 (1982), pp. 67-85. MR 649566 | Zbl 0484.13001

[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 796348 | Zbl 0573.13003

[15] M. Nagata, A treatise on the 14-th problem of Hilbert, Mem. Coll. Sci. Univ. Kyoto, 30 (1956), pp. 57-70. MR 88034 | Zbl 0089.02501

[16] M. Nagata, Some sufficient conditions for the fourteenth problem of Hilbert, Actas Del Coloquio Internac. Sobre Geometria Algebraica (1965), pp. 107-121. MR 199215 | Zbl 0142.28701

[17] C.P.L. Rhodes, On valuation subalgebras and their centres, Glasgow Math. J., 31 (1989), pp. 115-126. MR 981905 | Zbl 0668.13015

[18] C.P.L. Rhodes, Relatively Prüfer pairs of commutative rings, Comm. Algebra, 19 (1991), pp. 3423-3445. MR 1135634 | Zbl 0747.13013

[19] P. Schenzel, When is a flact algebra of finite type ?, Proc. Amer. Math. Soc., 109 (1990), pp. 287-290. MR 1000168 | Zbl 0711.13004