Integral Closure of Graded Integral Domains

REFERENCES

• Anderson , D. D. , Anderson , D. F. ( 1982 ). Divisibility properties of graded domains . Can. J. Math. 34 ( 1 ): 196 – 215 .
   Web of Science ®Google Scholar
• Bouvier , A. , Germain , G. ( 1979 ). A concise proof of a theorem of Mori–Nagata . C. R. Math. Rep. Acad. Sci. Canada 1 ( 6 ): 315 – 318 .
   Google Scholar
• Chang , G. W. , Kang , B. G. ( 2002 ). Integral closure of a ring whose regular ideals are finitely generated . J. Algebra 251 : 529 – 537 .
   Web of Science ®Google Scholar
• Eakin , P. M. Jr. , Heinzer , W. , Katz , D. , Ratliff , L. J. Jr. , ( 1987 ). Note on ideal-transforms, Rees rings, and Krull rings . J. Algebra 110 : 407 – 419 .
   Google Scholar
• Fanggui , W. , McCasland , R. L. ( 1997 ). On w-modules over strong Mori domains . Comm. Algebra 25 : 1285 – 1306 .
   Web of Science ®Google Scholar
• Fanggui , W. , McCasland , R. L. ( 1999 ). On strong Mori domains . J. Pure Appl. Algebra 135 : 155 – 165 .
   Web of Science ®Google Scholar
• Gilmer , R. ( 1972 ). Multiplicative Ideal Theory . New York : Dekker .
   Google Scholar
• Gilmer , R. ( 1984 ). Commutative Semigroup Rings . Chicago : University of Chicago Press .
   Google Scholar
• Goto , S. , Yamagishi , K. ( 1983 ). Finite generalization of a graded commutative ring . Proc. Amer. Math. Soc. 89 : 41 – 44 .
   Web of Science ®Google Scholar
• Huckaba , J. (1988). Commutative Rings with Zero Divisors . New York : Dekker.
   Google Scholar
• Kang , B. G. ( 1993 ). Integral closure of rings with zero divisors . J. Algebra 162 : 317 – 323 .
   Web of Science ®Google Scholar
• Kaplansky , I. ( 1970 ). Commutative Rings . Boston : Allyn and Bacon .
   Google Scholar
• Matijevic , J. R. ( 1976 ). Maximal ideal trasnformation of Noetherian rings . Proc. Amer. Math. Soc. 54 : 49 – 52 .
   Google Scholar
• Matsuda , R. ( 1999 ). The Mori-Nagata theorem for semigroups . Math. Japon. 49 ( 1 ): 17 – 19 .
   Google Scholar
• Nagata , M. ( 1962 ). Local Rings . New York : Interscience .
   Google Scholar
• Nishimura , J. ( 1976 ). Note on integral closure of a Noetherian domain . J. Math. Kyoto Univ. 16 ( 1 ): 117 – 122 .
   Google Scholar
• Northcott , D. G. ( 1968 ). Lessons on Rings, Modules and Multiplicities . Cambridge Univ. Press .
   Google Scholar
• Okon , J. S. , Rush , D. E. , Wallace , L. J. ( 2005 ). A Mori-Nagata theorem for lattices and graded rings . Houston J. Math. 31 ( 4 ): 973 – 997 .
   Web of Science ®Google Scholar
• Park , M. H. ( 2001 ). Group rings and semigroup rings over strong Mori domains . J. Pure Appl. Algebra 163 : 301 – 318 .
   Web of Science ®Google Scholar
• Park , M. H. ( 2002 ). On overrings of strong Mori domains . J. Pure Appl. Algebra 172 : 79 – 85 .
   Google Scholar
• Park , M. H. ( 2003 ). Power series rings over strong Mori domains . J. Algebra 270 ( 1 ): 361 – 368 .
   Web of Science ®Google Scholar
• Park , M. H. ( 2004 ). Group rings and semigroup rings over strong Mori domains II . J. Algebra 275 ( 2 ): 771 – 780 .
   Web of Science ®Google Scholar
• Querré , J. ( 1979 ). Sur la clôture intégrale des anneaux intègres noethériens . Bull. Sci. Math. 103 ( 2 ): 71 – 76 .
   Google Scholar
• Rush , D. E. ( 2003 ). Noetherian properties in monoid rings . J. Pure Appl. Algebra 185 : 259 – 278 .
   Web of Science ®Google Scholar
• Communicated by A. Facchini.
   Google Scholar