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A NOTE ON PRÜFER SEMISTAR MULTIPLICATION DOMAINS

Picozza, Giampaolo

  • 발행 : 2009.11.01

초록

In this note we give a new generalization of the notions of $Pr{\ddot{U}}fer$ domain and PvMD which uses quasi semistar invertibility, the "quasi P$\star$MD", and compare them with the P$\star$MD. We show in particular that the problem of when a quasi P$\star$MD is a P$\star$MD is strictly related to the problem of the descent to subrings of the P$\star$MD property and we give necessary and sufficient conditions.

키워드

semistar operation;star operation

참고문헌

  1. M. Zafrullah, Some polynomial characterizations of Prufer v-multiplication domains, J. Pure Appl. Algebra 32 (1984), no. 2, 231-237. https://doi.org/10.1016/0022-4049(84)90053-7
  2. S. El Baghdadi, M. Fontana, and G. Picozza, Semistar Dedekind domains, J. Pure Appl. Algebra 193 (2004), no. 1-3, 27-60. https://doi.org/10.1016/j.jpaa.2004.03.011
  3. M. Fontana and K. A. Loper, Nagata rings, Kronecker function rings, and related semistar operations, Comm. Algebra 31 (2003), no. 10, 4775-4805. https://doi.org/10.1081/AGB-120023132
  4. M. Griffin, Some results on v-multiplication rings, Canad. J. Math. 19 (1967), 710-722. https://doi.org/10.4153/CJM-1967-065-8
  5. A. Okabe and R. Matsuda, Semistar-operations on integral domains, Math. J. Toyama Univ. 17 (1994), 1-21.
  6. G. Picozza and F. Tartarone, When the semistar operation $\tilde{\star} $ is the identity, Comm. Algebra 36 (2008), no. 5, 1954-1975. https://doi.org/10.1080/00927870801941895
  7. J. Querre, Id´eaux divisoriels d'un anneau de polynomes, J. Algebra 64 (1980), no. 1, 270-284. https://doi.org/10.1016/0021-8693(80)90146-5
  8. F. Wang and R. L. McCasland, On w-modules over strong Mori domains, Comm. Algebra 25 (1997), no. 4, 1285-1306. https://doi.org/10.1080/00927879708825920
  9. G. Picozza, Star operations on overrings and semistar operations, Comm. Algebra 33 (2005), no. 6, 2051-2073. https://doi.org/10.1081/AGB-200063359
  10. G. Picozza, A note on semistar Noetherian domains, Houston J. Math. 33 (2007), no. 2, 415-432.
  11. J. R. Hedstrom and E. G. Houston, Pseudo-valuation domains, Pacific J. Math. 75 (1978), no. 1, 137-147. https://doi.org/10.2140/pjm.1978.75.137
  12. E. G. Houston, S. B. Malik, and J. L. Mott, Characterizations of *-multiplication domains, Canad. Math. Bull. 27 (1984), no. 1, 48-52. https://doi.org/10.4153/CMB-1984-007-2
  13. B. G. Kang, Prufer v-multiplication domains and the ring R[X]Nv , J. Algebra 123 (1989), no. 1, 151-170. https://doi.org/10.1016/0021-8693(89)90040-9
  14. R. Gilmer, An embedding theorem for HCF-rings, Proc. Cambridge Philos. Soc. 68 (1970), 583-587. https://doi.org/10.1017/S0305004100076568
  15. R. Gilmer, Multiplicative Ideal Theory, Corrected reprint of the 1972 edition. Queen's Papers in Pure and Applied Mathematics, 90. Queen's University, Kingston, ON, 1992.
  16. M. Fontana and J. A. Huckaba, Localizing systems and semistar operations, Non-Noetherian commutative ring theory, 169-197, Math. Appl., 520, Kluwer Acad. Publ., Dordrecht, 2000.
  17. M. Fontana, P. Jara, and E. Santos, Prufer $\ast$-multiplication domains and semistar operations, J. Algebra Appl. 2 (2003), no. 1, 21-50. https://doi.org/10.1142/S0219498803000349
  18. M. Fontana and G. Picozza, Semistar invertibility on integral domains, Algebra Colloq. 12 (2005), no. 4, 645-664. https://doi.org/10.1142/S1005386705000611
  19. J. T. Arnold and J. W. Brewer, Kronecker function rings and flat D[X]-modules, Proc. Amer. Math. Soc. 27 (1971), 483-485. https://doi.org/10.2307/2036479
  20. S. El Baghdadi and M. Fontana, Semistar linkedness and flatness, Prufer semistar multiplication domains, Comm. Algebra 32 (2004), no. 3, 1101-1126. https://doi.org/10.1081/AGB-120027969

피인용 문헌

  1. THE w-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGS vol.52, pp.4, 2015, https://doi.org/10.4134/JKMS.2009.46.6.1179
  2. On some classes of integral domains defined by Krullʼs a.b. operations vol.341, pp.1, 2011, https://doi.org/10.4134/JKMS.2009.46.6.1179