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Original Articles

Compositions of Consistent Systems of Rank One Discrete Valuation Rings

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Pages 2943-2964 | Received 25 Sep 2008, Published online: 18 Aug 2010

REFERENCES

  • Ciupercǎ , C. , Heinzer , W. J. , Ratliff , Jr. , L. J. , Rush , D. E. ( 2004 ). Projectively equivalent ideals and Rees valuations . J. Algebra 282 : 140 – 156 .
  • Ciupercǎ , C. , Heinzer , W. J. , Ratliff , Jr. , L. J. , Rush , D. E. ( 2006 ). Projectively full ideals in Noetherian rings . J. Algebra 304 : 73 – 93 .
  • Ciupercǎ , C. , Heinzer , W. J. , Ratliff , Jr. , L. J. , Rush , D. E. ( 2006 ). Projectively full ideals in Noetherian rings (II) . J. Algebra 305 : 974 – 992 .
  • Ciupercǎ , C. , Heinzer , W. J. , Ratliff , Jr. , L. J. , Rush , D. E. ( 2007 ). Projectively full ideals in Noetherian rings, a survey. Algebra, Geometry and their Interactions Contemporary Mathematics. Vol. 448. Amer. Math. Soc .
  • Endler , O. ( 1972 ). Valuation Theory . New York : Springer-Verlag .
  • Endler , O. ( 1975 ). Finite separable field extensions with prescribed valuations . Manuscripta Math. 17 : 383 – 408 .
  • Gilmer , R. ( 1990 ). Prüfer domains and rings of integer-valued polynomials . J. Algebra 129 : 502 – 517 .
  • Hasse , H. ( 1925 ). Zwei Existensatz uber algebraische Zahlkorper . Math. Ann. 95 : 229 – 238 .
  • Heinzer , W. J. , Ratliff , Jr. , L. J., Rush , D. E. ( 2007 ). Projectively full radical ideals in integral extension rings . J. Algebra 317 : 833 – 850 .
  • Heinzer , W. J. , Ratliff , Jr. , L. J. , Rush , D. E. ( 2008 ). Projective equivalence of ideals in Noetherian integral domains . J. Algebra 320 : 2349 – 2362 .
  • Krull , W. ( 1959 ). Über einen Existensatz der Bewertungstheorie . Abh. Math. Sem. Univ. Hamburg 23 : 29 – 55 .
  • Nagata , M. ( 1962 ). Local Rings . Interscience , New York : John Wiley .
  • Nagata , M. ( 1957 ). Note on a article of Samuel concerning asymptotic properties of ideals . Mem. Coll. Sci. Univ. Kyoto, Ser. A Math. 30 : 165 – 175 .
  • Rees , D. ( 1956 ). Valuations associated with ideals (II) . J. London Math. Soc. 36 : 221 – 228 .
  • Ribenboim , P. ( 1964 ). On the existence of fields with few discrete valuations . J. Reine Angew. Math. 216 : 45 – 49 .
  • Samuel , P. ( 1952 ). Some asymptotic properties of powers of ideals . Annals of Math 56 : 11 – 21 .
  • Swanson , I. , Huneke , C. ( 2006 ). Integral Closure of Ideals, Rings and Modules . Cambridge : Cambridge Univ. Press .
  • Walker , R. ( 1978 ). Algebraic Curves . New York : Springer-Verlag .
  • Zariski , O. , Samuel , P. ( 1958 ). Commutative Algebra . Vol. 1 . New York : D. Van Nostrand .
  • Communicated by I. Swanson.

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