본문 바로가기
KERD
논문KCI 등재

LOCALLY PSEUDO-VALUATION DOMAINS OF THE FORM D[X]Nv

장규환
대한수학회 (The Korean Mathematical Society)|2008.09|대한수학회지 (Journal of the KMS)|제45권 제5호|pp. 1405-1416

2

조회

0

다운로드

5

인용

0

참고문헌

키워드

UMT-domainthe ring D[X]Nvpseudo-valuation domain (PVD)(t-)locally PVD
주제분류수학

초록

Let D be an integral domain, X an indeterminate over D, Nv = {f ∈ D[X]|(Af )v = D}. Among other things, we introduce the concept of t-locally PVDs and prove that D[X]Nv is a locally PVD if and only if D is a t-locally PVD and a UMT-domain, if and only if D[X] is a t-locally PVD, if and only if each overring of D[X]Nv is a locally PVD.

Abstract

Let D be an integral domain, X an indeterminate over D, Nv = {f ∈ D[X]|(Af )v = D}. Among other things, we introduce the concept of t-locally PVDs and prove that D[X]Nv is a locally PVD if and only if D is a t-locally PVD and a UMT-domain, if and only if D[X] is a t-locally PVD, if and only if each overring of D[X]Nv is a locally PVD.

참고문헌 (28)

  1. D. F. Anderson, "Comparability of ideals and valuation overrings", Houston Journal of Mathematics, 5(4), pp.451~463 (1979)
  2. D. F. Anderson, "The class group of D +M", Journal of Pure and Applied Algebra, 52(3), pp.199~212 (1988)
  3. J. Arnold, "On the ideal theory of the Kronecker function ring and the domain D(X)", Canadian Journal of Mathematics, 21, pp.558~563 (1969)
  4. A. Badawi, "Remarks on pseudo-valuation rings", Communications in Algebra, 28(5), pp.2342~2358 (2000)
  5. V. Barucci, "On a class of Mori domains", Communications in Algebra, 11(17), pp.1989~2001 (1983)
  6. E. Bastida, "Overrings and divisorial ideals of rings of the form D +M", Michigan Math Journal, 20, pp.79~95 (1973)
  7. P.-J. Cahen, "On locally divided domains of the form Int(D)", Archiv der Mathematik (Basel), 74(3), pp.183~191 (2000)
  8. Nv, "Journal of Pure and Applied Algebra", 2005, 293~304
  9. G. W. Chang, "The w-integral closure of integral domains", Journal of Algebra, 295(1), pp.195~210 (2006)
  10. D. E. Dobbs, "Coherence, ascent of going-down, and pseudo-valuation domains", Houston Journal of Mathematics, 4(4), pp.551~567 (1978)
  11. D. E. Dobbs, "Locally pseudovaluation domains", Annali di Matematica Pura ed Applicata, 134, pp.147~168 (1983)
  12. D. E. Dobbs, "On t-linked overrings", Communications in Algebra, 20(5), pp.1463~1488 (1992)
  13. D. E. Dobbs, "t-linked overrings and Prufer v-multiplication domains", Communications in Algebra, 17(11), pp.2835~2852 (1989)
  14. M. Fontana, "UMT-domains and domains with Prufer integral closure", Communications in Algebra, 26(4), pp.1017~1039 (1998)
  15. M. Fontana, "Nagata rings, Kronecker function rings, and related semistar operations", Communications in Algebra, 31(10), pp.4775~4805 (2003)
  16. R. Gilmer, "Multiplicative Ideal Theory, Pure and Applied Mathematics, No. 12" (1972), Marcel Dekker, Inc.
  17. M. Griffin, "Some results on v-multiplication rings", Canadian Journal of Mathematics, 19, pp.710~722 (1967)
  18. J. R. Hedstrom, "Pseudo-valuation domains", Pacific Journal of Mathematics, 75(1), pp.137~147 (1978)
  19. J. R. Hedstrom, "no.2", Houston Journal of Mathematics, 4(2), pp.199~207 (1978)
  20. E. G. Houston, "On t-invertibility. II", Communications in Algebra, 17(8), pp.1955~1969 (1989)
  21. J. A. Huckaba, "Commutative Rings with Zero Divisors, Monographs and Textbooks in Pure and Applied Mathematics", pp.117~ (1988), Marcel Dekker, Inc.
  22. Nv, "Journal of Algebra", 1989, 151~170
  23. I. Kaplansky, "Commutative Rings" (1974), The University of Chicago Press
  24. H. Kim, "Some remarks on pseudo-Krull domains", Communications in Algebra, 33(6), pp.1745~1751 (2005)
  25. A. Okabe, "Note on strong pseudo-valuation domains", Bulletin of the Faculty of Science Ibaraki University. Series A, (21), pp.9~12 (1989)
  26. J. Querr´e, "Sur une propi´et´e des anneaux de Krull", Bulletin des Sciences Mathématiques, 95(2), pp.341~354 (1971)
  27. F. Wang, "On induced operations and UMT-domains", Sichuan Shifan Daxue Xuebao Ziran Kexue Ban, 27(1), pp.1~9 (2004)
  28. M. Zafrullah, "Putting t-invertibility to use, Non-Noetherian commutative ring theory", Applied mathematics, 520, pp.429~457 (2000), Kluwer Acad. Publ.

관련 논문AI추천

On almost pseudo-valuation domains, II장규환강원경기수학회 · 한국수학논문집2011 · 제19권 제4호Locally divided domains of the form D[X]Nv장규환강원경기수학회 · 한국수학논문집2010 · 제18권 제1호On almost pseudo-valuation domains장규환강원경기수학회 · 한국수학논문집2010 · 제18권 제2호Power series rings over Pr\"ufer $v$-multiplication domains장규환대한수학회 · 대한수학회지2016 · 제53권 제2호A Note on S-Noetherian Domains임정욱경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제3호Finitely t-valuative domains장규환강원경기수학회 · 한국수학논문집2014 · 제22권 제4호

이 간행물의 다른 논문 (16건)

Weighted composition operators on weighted spaces of vector-valued analytic functionsJasbir Singh Manhaspp. 1203-1220Projective domains with non-compact automorphism groups I이창우pp. 1221-1241A construction of one-factorization임선주, 최윤영, 김상목, 박봉주pp. 1243-1253The BFK-gluing formula for zeta-determinants and the value of relative zeta functions at zero이윤원pp. 1255-1274Monotone iteration scheme for impulsive three-point nonlinear boundary value problems with quadratic convergenceDoa'A Garout, Bashir Ahmad, Ahmed Alsaedipp. 1275-1295
원문 보기