Riassunto
SiaR un dominioZ-graduato, noetheriano. Questo articolo tratta principalmente il gruppo di classi di divisori di localizzazioni e completamenti rispetto ad una topologia α-adica (α omogeneo) diR. Alcuni risultati tecnici vengono applicati allo studio dei sottoanelli Veronesiani diR.
Summary
LetR be aZ-graded, noetherian, integral domain. This paper deals mainly with the divisor class groups of localizations and completions with respect to an α-adic topology (α homogeneous) ofR. Some technical results are used to study the Veronesean subrings ofR.
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References
D. D. Anderson—D. F. Anderson,Divisorial ideals and invertible ideals in a graded integral domains, J. Algebra,76 (1982), pp.549–569.
D. F. Anderson,Graded Krull domains, Comm. Algebra,7 (1979), pp. 79–106.
M. Arezzo—S. Greco,Sul gruppo delle classi di ideali, Ann. Sc. Norm. Sup. Pisa,21 (1967), pp. 459–483.
N. Bourbaki,Algèbre commutative, Ch. I–VII, Hermann, Paris (1961–1965).
M. P. Cavaliere,Sui moduli liberi e proiettivi graduati, Boll. U.M.I., (5),14-A (1977), pp. 82–91.
M. P. Cavaliere,Sulle A-successioni massimali omogenee in un anello graduato, Rend. Sem. Mat. Univ. Politecn. Torino,37 (1979), pp. 33–45.
M. P. Cavaliere—G. Niesi,On Serre's conditions in the form ring of an ideal, J. Math. Kyoto Univ.,21 (1981), pp. 537–546.
U. Daepp—A. Evans,A note on Buchsbaum rings and localizations of graded domains, Can. J. Math.,32 (1980), pp. 1244–1249.
M. Fiorentini,Esempi di anelli di Cohen-Macaulay semifattoriali che non sono di Gorenstein. Rend. Acc. Lincei, 5 (1971), pp. 244–249.
R. Fossum,The divisor class group of a Krull domain, Springer-Verlag, New York (1973).
A. V. Geramita—C. Small,Introduction to homological methods in commutative rings, Queen's papers n. 43, Kingston (1976).
S. Goto—K. Watanabe,On graded rings, I, J. Math. Soc. Japan,30 (1978), pp. 179–213.
S. Greco,Sull'integrità e la fattorialità dei completamenti m-adici, Rend. Sem. Mat. Univ. Padova,36 (1966), pp. 50–65.
S. Greco,Sugli ideali frazionari invertibili, Rend. Sem. Mat. Univ. Padova,36 (1966), pp. 315–333.
A. Grothendieck—J. A. Dieudonné,Eléments de géométrie algébrique, vol. I, Springer-Verlag, Berlin (1971).
I. Kaplansky,Commutative rings, Univ. Chicago Press (1970).
W. E. Kuan,Some results on normality of a graded ring, Pac. J. Math.,64 (1976), pp. 455–463.
J. Lipman,Rings with discrete divisor class group: theorem of Danilov-Samuel, Amer. J. Math.,101 (1979), pp. 203–211.
J. Matijevich—P. Roberts,A conjecture of Nagata on graded Cohen-Macaulay rings, J. Math. Kyoto Univ.,14 (1974), pp. 125–128.
H. Matsumura,Commutative Algebra, Benjamin, New York (1970).
J. L. Mott,Multiplication rings containing only finitely many minimal prime ideals, J. Sch. Hiroshima Univ. Ser. A-1,33 (1969), pp. 73–83.
C. Nastasescu—F. Van Oystaeyen,Graded ring theory, North Holland, Amsterdam (1982).
J. Ohm,Space curve as ideal-theoretic complete intersections, Studies in Math., vol.20, Math. Ass. Amer. (1980), pp. 47–115.
D. Portelli—W. Spanger,Condizioni di fattorialità ed anello graduato associato ad un ideale, Ann. Univ. Ferrara,28 (1982), pp. 181–195.
J. J. Rotman,An Introduction to Homological Algebra, Academic Press, New York (1979).
P. Samuel,Sur les anneaux factoriels, Bull. Soc. Math. France,89 (1961), pp. 155–173.
S. Yuan,Reflexive modules and Algebra Class group over noetherian integrally closed domains, J. Algebra,32 (1974), pp. 405–417.
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Portelli, D., Spangher, W. On the divisor class groups of localizations, completions and veronesean subrings of z-graded krull domains. Ann. Univ. Ferrara 30, 97–118 (1984). https://doi.org/10.1007/BF02853274
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DOI: https://doi.org/10.1007/BF02853274