Results on the Ratliff–Rush Closure and the Integral Closedness of Powers of Certain Monomial Curves

REFERENCES

• Al-Ayyoub , I. ( 2009 ). Reduced Gröbner bases of certain toric varieties; A New Short Proof . Comm. Algebra 37 : 2945 – 2955 .
   Web of Science ®Google Scholar
• Al-Ayyoub , I. ( 2009 ). An algorithm for computing the Ratliff–Rush closure . Journal of Algebra and its Applications 8 : 521 – 532 .
   Web of Science ®Google Scholar
• Al-Ayyoub , I. ( 2009 ). Normality of monomial ideals . Rocky Mountain Journal of Math. 39 : 1 – 9 .
   Google Scholar
• Al-Ayyoub , I. ( 2010 ). The Ratliff–Rush closure of initial ideals of certain prime ideals . Rocky Mountain Journal of Math. 40 : 1085 – 1093 .
   Google Scholar
• Al-Ayyoub , I. ( 2004 ). The Ratliff–Rush closure and a minimal Groebner basis for the defining ideals of certain affine monomial curves. Ph.D. thesis, New Mexico State University. Las Cruces, NM .
   Google Scholar
• Corso , A. , Huneke , C. , Vasconcelos , W. ( 1998 ). On the integral closure of ideals . Manuscripta Math. 95 : 331 – 347 .
   Google Scholar
• Crispin Quiñonez , V. ( 2007 ). Ratliff–Rush monomial ideals . Algebraic and Geometric Combinatorics, Contemp. Math. 423 : 43 – 50 .
   Google Scholar
• Elias , J. ( 2004 ). On the computations of the Ratliff–Rush closure . J. Symbolic Comput. 37 : 717 – 725 .
   Web of Science ®Google Scholar
• Ghezzi , L. ( 2002 ). On the depth of the associated graded ring of an ideal . J. Algebra 248 : 688 – 707 .
   Google Scholar
• Heinzer , W. , Lantz , D. , Shah , K. ( 1992 ). The Ratliff–Rush ideals in a Noetherian ring . Comm. Algebra 20 : 591 – 622 .
   Web of Science ®Google Scholar
• Heinzer , W. , Johnston , B. , Lantz , D. , Shah , K. ( 1993 ). Coefficient ideals in and blowups of a commutative Noetherian domain . J. Algebra 162 : 355 – 391 .
   Web of Science ®Google Scholar
• Huckaba , S. , Marley , T. ( 1997 ). Hilbert coefficients and the depths of associated graded rings . J. London Math. Soc. 56 : 64 – 76 .
   Web of Science ®Google Scholar
• Huneke , C. (1982). On the associated graded ring of an ideal. Illinois J. Math. 26:121–137.
   Web of Science ®Google Scholar
• Patil , D. P. ( 1993 ). Minimal sets of generators for the relation ideals of certain monomial curves . Manuscripta Math. 80 : 239 – 248 .
   Web of Science ®Google Scholar
• Patil , D. P. , Roberts , L. G. ( 2003 ). Hilbert functions of monomial curves . Journal of Pure and Applied Algebra 183 : 257 – 292 .
   Google Scholar
• Patil , D. P. , Singh , B. ( 1990 ). Generators for the derivation modules and the relation ideals of certain curves . Manuscripta Math. 68 : 327 – 335 .
   Web of Science ®Google Scholar
• Patil , D. P. , Tamone , G. ( 2004 ). On the H-polynomial of certain monomial curves . Rocky Mountain Journal of Math. 34 : 289 – 308 .
   Google Scholar
• Patil , D. P. , Tamone , G. ( 2002 ). On the type of the associated graded ring of certain monomial curves . Comm. Algebra 30 : 5181 – 5198 .
   Web of Science ®Google Scholar
• Ratliff , R. J. , Rush , D. E. ( 1978 ). Two notes on reductions of ideals . Indiana Univ. Math. J. 27 : 929 – 934 .
   Web of Science ®Google Scholar
• Reid , L. , Roberts , L. G. , Vitulli , M. A. ( 2003 ). Some results on normal monomial ideals . Comm. Algebra 31 : 4485 – 4506 .
   Web of Science ®Google Scholar
• Rossi , M. E. , Swanson , I. ( 2003 ). Notes in the behavior of the Ratliff–Rush filtration . Contemporary Math. 331 : 313 – 328 .
   Google Scholar
• Sengupta , I. ( 2003 ). A Gröbner basis for certain affine monomial curves . Comm. Algebra 31 : 1113 – 1129 .
   Web of Science ®Google Scholar
• Sengupta , I. ( 2003 ). A minimal free resolution of certain momomial curves in 𝔸4 . Comm. Algebra 31 : 2791 – 2809 .
   Web of Science ®Google Scholar
• Sturmfels , B. ( 1995 ). Gröbner Bases and Convex Polytopes . Providence , RI : Amer. Math. Soc .
   Google Scholar
• Sturmfels , B. ( 1991 ). Gröbner bases of toric varieties . Tohoku Mathematical Journal 43 : 249 – 261 .
   Web of Science ®Google Scholar
• Swanson , I. , Huneke , C. ( 2006 ). Integral Closure of Ideals, Rings, and Modules . Cambridge : Cambridge University Press .
   Google Scholar
• Vitulli , M. A. Some normal monomial ideals . Contemp. Math. 324 , Providence: Amer. Math. Soc., pp. 205–217 .
   Google Scholar
• Communicated by R. Wiegard.
   Google Scholar