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On piecewise Noetherian domains

Hwankoo Kim|Fanggui Wang|장규완
대한수학회 (The Korean Mathematical Society)|2016.05|대한수학회지 (Journal of the KMS)|제53권 제3호|pp. 623-643

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참고문헌

키워드

piecewise Noetherian ringNoetherian spectrumpiecewise $w$-Noetherian domainstrong Mori spectrum
주제분류수학

초록

In this paper, we study piecewise Noetherian (resp., piecewise $w$-Noetherian) properties in several settings including flat (resp., $t$-flat) overrings, Nagata rings, integral domains of finite character (resp., $w$-finite character), pullbacks of a certain type, polynomial rings, and $D+XK[X]$ constructions.

Abstract

In this paper, we study piecewise Noetherian (resp., piecewise $w$-Noetherian) properties in several settings including flat (resp., $t$-flat) overrings, Nagata rings, integral domains of finite character (resp., $w$-finite character), pullbacks of a certain type, polynomial rings, and $D+XK[X]$ constructions.

참고문헌 (27)

  1. D. D. Anderson, "Integral domains of finite t-character", J. Algebra, 396, pp.169~183 (2013)
  2. D. D. Anderson, "The Krull intersection Theorem. II", Pacific J. Math, 66(1), pp.15~22 (1976)
  3. J. T. Arnold, "On flat overrings, ideal transforms and generalized transforms of a commutative ring", J. Algebra, 18, pp.254~264 (1971)
  4. J. A. Beachy, "Piecewise Noetherian rings", Comm. Algebra, 12(21-22), pp.2679~2706 (1984)
  5. J. A. Beachy, "A note on prime ideals which test injectivity", Comm. Algebra, 15(3), pp.471~478 (1987)
  6. A. Benhissi, "CCA pour les id´eaux radicaux et divisoriels", Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 44(92)(2), pp.119~135 (2001)
  7. Nv, "J. Pure Appl. Algebra", 2005, 293~304
  8. "J. Algebra", 1978, 423~439
  9. M. D’Anna, "Commutative algebra and its applications", pp.155~172 (2009), Walter de Gruyter
  10. D. E. Dobbs, "t-linked overrings and Pr¨ufer v-multiplication domains", Comm. Algebra, 17(11), pp.2835~2852 (1989)
  11. S. El Baghdadi, "Ring-theoretic properties of PvMDs", Comm. Algebra, 35(5), pp.1607~1625 (2007)
  12. S. El Baghdadi, "A note on generalized Krull domains", J. Algebra Appl, 13(7), pp.18~ (2014)
  13. A. Facchini, "Generalized Dedekind domains and their injective modules", J. Pure Appl. Algebra, 94(2), pp.159~173 (1994)
  14. M. Fontana, "On the class group and the local class group of a pullback", J. Algebra, 181(3), pp.803~835 (1996)
  15. R. Gilmer, "Multiplicative Ideal Theory" (1972), Marcel Dekker
  16. E. Houston, "On t-invertibility II", Comm. Algebra, 17(8), pp.1955~1969 (1989)
  17. Nv, "J. Algebra", 1989, 151~170
  18. 김환구, "Integral domains which are t-locally Noetherian", 충청수학회지, 24(4), pp.843~848 (2011), 충청수학회
  19. 김환구, "A NOTE ON ZERO DIVISORS IN w-NOETHERIAN-LIKE RINGS", 대한수학회보, 51(6), pp.1851~1861 (2014), 대한수학회
  20. D. J. Kwak, "On t-flat overrings", Chinese J. Math, 23(1), pp.17~24 (1995)
  21. C. P. Lu, "Modules satisfying ACC on a certain type of colons", Pacific J. Math, 131(2), pp.303~318 (1988)
  22. C. P. Lu, "Modules and rings satisfying (accr)", Proc. Amer. Math. Soc, 117(1), pp.5~10 (1993)
  23. J. Ohm, "Rings with Noetherian spectrum", Duke Math. J, 35, pp.631~639 (1968)
  24. M. H. Park, "Power series rings over strong Mori domains", J. Algebra, 270(1), pp.361~368 (2003)
  25. A. C. Pearson, "Noncommutative Piecewise Noetherian Rings", 박사, pp.2011
  26. M. Tamekkante, "Chain conditions in amalgamated algebras along an ideal", Arab. J. Math, 2(4), pp.403~408 (2013), Springer
  27. F. Wang, "On w-modules over strong Mori domains", Comm. Algebra, 25(4), pp.1285~1306 (1997)

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