References
- Bishop , W. , Petro , J.W. , Ratliff , L.J. Jr and Rush , D.E. 1989 . Note on noetherian filtrations . Comm. Algebra , 17 ( 2 ) : 471 – 485 .
- Brodmann , M. 1979 . The asymptotic nature of the analytic spread . Math. Proc. Camb. Philos.Soc , 86 ( 2 ) : 35 – 39 .
- Bruns , W. and Herzog , J. 1993 . Cohen-Macaulay rings . Camb. studies in adv. math , 39 ( 2 )
- Dichi , H. 1989 . Integral dependence over a filtration . J. Pure Appl. Algebra , 58 ( 2 ) : 7 – 18 .
- Dichi , H. 1995 . Integral closure of a filtration relative to a module . Comm. Algebra , 23 ( 2 ) : 3145 – 3153 .
- Dichi , H. 1995 . About the prüferian closure of a filtration on a one dimensional noetherian ring . Arch. Math , 65 ( 2 ) : 379 – 383 .
- Diagana , Y. , Dichi , H. and Sangaré , D. 1994 . Filtrations, Generalized analytic independence, analytic spread . Afrika Matematika , 4 ( 2 ) : 101 – 114 . serie 3
- Sangaré , D. 1991 . Filtrations, asymptotic and prüferian closures, cancellation laws . Proc. Amer. Math. Soc , 113 ( 3 ) : 617 – 624 .
- Dichi , H. and Sangaré , D. 1991 . Hilbert functions, Hilbert-Samuel quasi- polynomials with respect to f-good filtrations, multiplicities . J. Pure Appl. Algebra , 113 ( 3 ) to appear
- Diehi , H. and Sangaré , D. 1992 . Filtrations, integral dependence, reductionf-good filtrations . Comm. Algebra , 20 ( 8 ) : 2393 – 2418 .
- Eakin , P. 1968 . The converse of a well known theorem on noetherian rings . Math. Ann , 177 ( 8 ) : 278 – 282 .
- Goto , Shiro and Nishida , Koji . 1994 . The Cohen- Macaulay and Gorenstein Rees Algebras Associated to Filtrations . Mem. Amer. Math. Soc , 110 ( 526 )
- Huneke , C. 1982 . On the Finite Generation of Symbolic Blow tips . Math, Z , 179 ( 526 ) : 465 – 472 .
- Mc Adam , S. “ Asymptotic prime divisors ” . In Lecture Notes in Math , Vol. 1023 , Springer- Verlag .
- Northcott , D.G. and Rees , D. 1954 . Reduction of ideals in a local ring . Proc. Camb. Philos. Soc , 50 : 145 – 158 .
- Okon , J.S. 1984 . Prime divisors, analytic spread and filtrations . Pacific J. Math , 113 ( 2 ) : 451 – 462 .
- Okon , J.S. and Ratliff , L.J. Jr . 1988 . Filtrations, closure operation and prime divisors . Math, Proc. Camb. Philos. Soc , 104 ( 2 ) : 31 – 46 .
- Okon , J.S. and Rathft , L.J. Jr . 1990 . Reduction of filtrations . Pacific J. Math , 144 ( 1 ) : 137 – 154 .
- Okon , J.S. and Ratliff , L.J. Jr . 1991 . On the grade and cograde of a noetherian filtration . Nagoya Math, J , 122 ( 1 ) : 43 – 62 .
- Petro , J.W. 1961 . “ Some results in the theory of pseudo valuations ” . In Ph.D , Iowa : State Univ . Graduate College
- Ratliff , J Louis Jr . 1989 . ▵-closure of ideals and rings . Trans. Amer. Math. Soc , 313 ( 1 ) : 221 – 247 .
- Rees , D. 1955 . Valuations associated with a local ring (I) . Proc. London Math. Soc , 5 ( 3 ) : 107 – 128 .