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Asymptotic for the number of star operations on one-dimensional Noetherian domains

Dario Spirito
대한수학회 (The Korean Mathematical Society)|2021.09|대한수학회지 (Journal of the KMS)|제58권 제5호|pp. 1239-1260|DOI 10.4134/JKMS.j200543

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키워드

Star operationsmultiplicative operationsNoetherian domains
주제분류수학

초록

We study the set of star operations on local Noetherian domains $D$ of dimension $1$ such that the conductor $(D:T)$ (where $T$ is the integral closure of $D$) is equal to the maximal ideal of $D$. We reduce this problem to the study of a class of closure operations (more precisely, multiplicative operations) in a finite extension $k\subseteq B$, where $k$ is a field, and then we study how the cardinality of this set of closures vary as the size of $k$ varies while the structure of $B$ remains fixed.

Abstract

We study the set of star operations on local Noetherian domains $D$ of dimension $1$ such that the conductor $(D:T)$ (where $T$ is the integral closure of $D$) is equal to the maximal ideal of $D$. We reduce this problem to the study of a class of closure operations (more precisely, multiplicative operations) in a finite extension $k\subseteq B$, where $k$ is a field, and then we study how the cardinality of this set of closures vary as the size of $k$ varies while the structure of $B$ remains fixed.

참고문헌 (22)

  1. D. D. Anderson, "Non-Noetherian commutative ring theory", pp.1~31 (2000), Kluwer Acad. Publ
  2. Hyman Bass, "On the ubiquity of Gorenstein rings", Mathematische Zeitschrift, 82(1), pp.8~28 (1963), Springer Science and Business Media LLC[DOI]
  3. Marco Fontana, "Star operations and pullbacks", Journal of Algebra, 274(1), pp.387~421 (2004), Elsevier BV[DOI]
  4. R. Gilmer, "Multiplicative Ideal Theory" (1972), Marcel Dekker, Inc
  5. R. L. Graham, "Handbook of Combinatorics. Vol. 1, 2" (1995), Elsevier Science B.V
  6. William J. Heinzer, "M-Canonical ideals in integral domains", Communications in Algebra, 26(9), pp.3021~3043 (1998), Informa UK Limited[DOI]
  7. Evan Houston, "Integral Domains Which Admit at Most Two Star Operations", Communications in Algebra, 39(5), pp.1907~1921 (2011), Informa UK Limited[DOI]
  8. Evan Houston, "Noetherian domains which admit only finitely many star operations", Journal of Algebra, 366, pp.78~93 (2012), Elsevier BV[DOI]
  9. Evan Houston, "Integrally Closed Domains with Only Finitely Many Star Operations", Communications in Algebra, 42(12), pp.5264~5286 (2014), Informa UK Limited[DOI]
  10. Evan Houston, "A characterization of local Noetherian domains which admit only finitely many star operations: The infinite residue field case", Journal of Algebra, 407, pp.105~134 (2014), Elsevier BV[DOI]
  11. T. W. Hungerford, "On the structure of principal ideal rings", Pacific J. Math, 25, pp.543~547 (1968)
  12. Wolfgang Krull, "Beiträge zur Arithmetik kommutativer Integritätsbereiche", Mathematische Zeitschrift, 41(1), pp.545~577 (1936), Springer Science and Business Media LLC[DOI]
  13. E. Matlis, "Re exive domains", J. Algebra, 8, pp.1~33 (1968)[DOI]
  14. E. Matlis, "1-dimensional Cohen-Macaulay rings, Lecture Notes in Mathematics, Vol. 327" (1973), Springer-Verlag
  15. Mi Hee Park, "On the cardinality of star operations on a pseudo-valuation domain", Rocky Mountain Journal of Mathematics, 42(6), pp.1939~1951 (2012), Rocky Mountain Mathematics Consortium[DOI]
  16. P. Samuel, "Sur les anneaux factoriels", Bull. Soc. Math. France, 89, pp.155~173 (1961)
  17. Dario Spirito, "STAR OPERATIONS ON KUNZ DOMAINS", International Electronic Journal of Algebra, pp.171~185 (2019), The International Electronic Journal of Algebra[DOI]
  18. Dario Spirito, "Vector subspaces of finite fields and star operations on pseudo-valuation domains", Finite Fields and Their Applications, 56, pp.17~30 (2019), Elsevier BV[DOI]
  19. Dario Spirito, "The sets of star and semistar operations on semilocal Prüfer domains", Journal of Commutative Algebra, 12(4), pp.581~602 (2020), Rocky Mountain Mathematics Consortium[DOI]
  20. Dario Spirito, "Multiplicative closure operations on ring extensions", Journal of Pure and Applied Algebra, 225(4), pp.106555~ (2021), Elsevier BV[DOI]
  21. R. P. Stanley, "Enumerative combinatorics. Volume 1" (2012), Cambridge University Press
  22. B. White, "Star operations and numerical semigroup rings", PhD, pp.2014

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