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In questo lavoro viene studiata l'operazione di somma amalgamata [13] di spazi spettrali [24] e vengono esaminate in dettaglio alcune proprietà algebriche degli anelli che interi vengono in tale operazione. Dei risultati ottenuti vengono poi fornite numerose applicazionalla teoria dei « D + m » domini diGilmer [19], a quella della seminormalizzazione diTra verso [38] e a quella delle CPI-estensioni nel senso diBoisen-Sheldon [5].
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References
S.Anantharaman,Schémas en groupes, espaces homogènes et espaces algébriques sur une base de dimension 1, Thèse, 1971.
A. Andreotti -E. Bombieri,Sugli omeomorfismi delle varietà algebriche, Ann. Sc. Norm. Sup. Pisa,23 (1969), pp. 430–450.
M. F. Atiyah -I. G. MacDonald,Introduction to commutative algebra, Addison-Wesley, Reading 1969.
C. E. Aull -W. J. Thron,Separation axioms between T 0 and T 1 Indag. Math.,24 (1962), pp. 26–37.
M. B. Boisen -P. B. Sheldon,CPI-extensions: overrings of integral domains with special prime spectrum, Canad. J. Math.,29 (1977), pp. 722–737.
N. Bourbaki,Algèbre commutative, Hermann, Paris, 1961–1965.
N. Bourbaki,Topologie générale, Ch. 1–4, Hermann, Paris 1971.
A.Bouvier - M.Fontana,Une classe d'espaces spectraux de dimension 1:les espaces principaux, (à paraître).
A. Conte,Proprietà di separazione della topologia di Zariski di uno schema, Rend. Ist. Lombardo A106 (1972), pp. 79–111.
J.Dieudonné,Topics in local algebra, Notre Dame Math. Lect. Notes, 1967.
D. E. Dobbs,On going down for simple overrings II, Comm. Algebra1 (1974), pp. 439–458.
D. E. Dobbs -I. J. Papick,On going down for simple overrings III, Proc. AMS,54 (1976), pp. 35–38.
J. Dugundji,Topology, Allyn and Bacon, Boston 1969.
S. Endô,Note on p.p. rings (a supplement to Hattori's paper), Nagoya Math. J.,17 (1960), pp. 167–170.
S. Endô,On semi-hereditary rings, J. Math. Soc. Japan,13 (1961), pp. 109–119.
S. Endô,Projective modules over polynomials rings, J. Math. Soc. Japan,15 (1963), pp. 339–395.
D.Ferrand,Conducteur, descente et pincement, Thèse.
M. Fontana -P. Maroscia,Sur les anneaux de Goldman, Boll. U.M.I.,13 B (1976), pp. 743–759.
R. Gilmer,Multiplicative ideal theory, Queen's Univ. Press, Kingston 1968.
R. Gilmer,A class of domains in which primary ideals are valuation ideals, Math. Ann.,161 (1965), pp. 247–254.
R. Gilmer -E. Bastida,Overrings and divisorial ideals of rings of the form D + M, Michigan Math. J.,20 (1974), pp. 79–95.
R. Gilmer -W. J. Heinzer,Intersections of quotient rings of an integral domain, J. Math. Kyoto Univ.,7 (1967), pp. 133–150.
A. Grothendieck -J. Dieudonne,Eléments de géométrie algébrique I, Springer, Berlin 1971.
M. Hochster,Prime ideal structure in commutative rings, Trans. AMS,142 (1969), pp. 46–60.
I. Kaplansky,Commutative rings, Allyn and Bacon, Boston 1970.
I. Kikuchi,Some remarkes on S-domains, J. Math. Kyoto Univ.,6 (1966), pp. 49–60.
W. J. Lewis,The spectrum of a rings as a partially ordered set, J. Algebra,25 (1973), pp. 419–434.
W. J. Lewis -J. Ohm,The ordering of Spec R, Canad. J. Math.,28 (1976), pp. 820–835.
P.Maroscia,Topological properties of some classes of G-domains, (to appear).
M. Nagata,Local rings, Interscience, New York 1962.
J. P. Olivier,Anneaux absolument plats universels et épimorphismes d'anneaux, C. R. Acad. Sci. Paris,266 (1968), pp. A317–318.
I. J. Papick,Topologically defined classes of going-down domains, Trans. AMS,219 (1976), pp. 1–37.
C. Pedrini,Incollamenti di ideali primi e gruppi di Picard, Rend. Sem. Mat. Univ. Padova,48 (1973), pp. 39–66.
R. L. Pendleton,A characterization of Q-domains, Bull. AMS,72 (1966), pp. 499–500.
G. Picavet,Sur les anneaux commutatifs dont tout idéal premier est de Goldman, C. R. Acad. Sci. Paris,280 (1975), pp. A 1719–1721.
R. Ramaswamy -T. M. Viswanathan,Overring properties of G-domains, Proc. AMS,58 (1976), pp. 59–66.
G. Tamone,Sugli incollamenti di ideali primi, Boll. U.M.I.,14 B (1977), pp. 810–825.
C. Traverso,Seminormality and Picard group, Ann. Sc. Norm. Sup. Pisa,24 (1970), pp. 585–595.
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Work performed under the auspices of C.N.R. (Gruppo Nazionale per le Strutture Algebriche, Geometriche e loro Applicazioni).
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Fontana, M. Topologically defined classes of commutative rings. Annali di Matematica pura ed applicata 123, 331–355 (1980). https://doi.org/10.1007/BF01796550
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DOI: https://doi.org/10.1007/BF01796550