Classes of commutative rings characterized by going-up and going-down behavior
Dobbs, David E. ; Fontana, Marco
Rendiconti del Seminario Matematico della Università di Padova, Tome 68 (1982), p. 113-127 / Harvested from Numdam
Publié le : 1982-01-01
@article{RSMUP_1982__66__113_0,
     author = {Dobbs, David E. and Fontana, Marco},
     title = {Classes of commutative rings characterized by going-up and going-down behavior},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {68},
     year = {1982},
     pages = {113-127},
     mrnumber = {664575},
     zbl = {0483.13001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1982__66__113_0}
}
Dobbs, David E.; Fontana, Marco. Classes of commutative rings characterized by going-up and going-down behavior. Rendiconti del Seminario Matematico della Università di Padova, Tome 68 (1982) pp. 113-127. http://gdmltest.u-ga.fr/item/RSMUP_1982__66__113_0/

[1] G. Artico - U. Marconi, On the compactness of minimal spectrum, Rend. Sem. Mat. Univ. Padova, 56 (1977), pp. 79-84. | Numdam | MR 480463 | Zbl 0381.13003

[2] C.E. Aull - W.J. Thron, Separation axioms between T0 and T1, Indagat. Math., 24 (1962), pp. 26-37. | MR 138082 | Zbl 0108.35402

[3] M. Auslander, On regular group rings, Proc. Amer. Math. Soc., 8 (1957), pp. 658-664. | MR 87670 | Zbl 0079.26703

[4] N. Bourbaki, Algèbre Commutative, Chs. 1-2, Hermann, Paris, 1961.

[5] A. Conte, Proprietà di separazione della topologia di Zariski di uno schema, Rend. Ist. Lombardo Sc. A, 106 (1972), pp. 79-111. | MR 349670 | Zbl 0254.14002

[6] G. De MARCO - A. ORSATTI, Commutative rings in which every prime ideal is contained in a unique maximal ideal, Proc. Amer. Math. Soc., 30 (1971), pp. 459-466. | MR 282962 | Zbl 0219.13003

[7] D.E. Dobbs - I. J. PAPICK, Going-down: a survey, Nieuw Arch. Wisk., 26 (1978), pp. 255-291. | MR 491656 | Zbl 0383.13005

[8] M. Fontana, Topologically defined classes of commutative rings, Annali Mat. Pura Appl., 123 (1980), pp. 331-355. | MR 581935 | Zbl 0443.13001

[9] M. Harada, Note on the dimension of modules and algebras, J. Inst. Polytech. Osaka City Univ. A, 7 (1956), pp. 17-27. | MR 81269 | Zbl 0079.26702

[10] B.W. Irlbeck, Finitely generated projective ideals in commutative rings, J. Reine Angew. Math., 298 (1978), pp. 98-100. | MR 485829 | Zbl 0366.13003

[11] I. Kaplansky, Commutative Rings, Allyn and Bacon, Boston, 1970. | MR 254021 | Zbl 0203.34601

[12] J.A. Kist, Minimal prime ideals in commutative semigroups, Proc. London Math. Soc., (3), 13 (1963), pp. 31-50. | MR 143837 | Zbl 0108.04004

[13] W.J. Lewis, The spectrum of a ring as a partially ordered set, J. Algebra, 25 (1973), pp. 419-434. | MR 314811 | Zbl 0266.13010

[14] W.J. Lewis - J. OHM, The ordering of Spec (R), Canad. J. Math., 28 (1976), pp. 820-835. | MR 409428 | Zbl 0313.13003

[15] T.P. Speed, A note on commutative Baer rings, J. Austral. Math. Soc., 14 (1972), pp. 257-263. | MR 318120 | Zbl 0242.13003

[16] W.V. Vasconcelos, Finiteness in projective ideals, J. Algebra, 25 (1973), pp. 269-278. | MR 314828 | Zbl 0254.13012