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SEMISTAR OPERATIONS ON ALMOST PSEUDO-VALUATION DOMAINS

Year 2011, Volume: 10 Issue: 10, 37 - 55, 01.12.2011

Abstract

We characterize when an almost pseudo-valuation domain has a finite number of semistar operations.

References

  • A. Badawi and E. Houston, Powerful ideals, strongly primary ideals, almost pseudo-valuation domains, and conducive domains, Comm. Alg., 30 (2002), 1606.
  • M. Fontana and K. Loper, Kronecker function rings: a general approach, Ideal Theoretic Methods in Commutative Algebra, Lecture Notes in Pure and Appl. Math., 220, M. Dekker, New York, 2001, 189-205.
  • M. Fontana and K. Loper, An historical overview of Kronecker function rings, Nagata rings, and related star and semistar operations, Multiplicative Ideal Theory in Commutative Algebra, Springer, New York, 2006, 169-187.
  • R. Gilmer, Multiplicative Ideal Theory, M. Dekker, New York, 1972.
  • F. Halter-Koch, Ideal Systems: An Introduction to Multiplicative Ideal The- ory, M. Dekker, New York, 1998.
  • J. Hedstrom and E. Houston, Pseudo-valuation domains, PaciŞc J. Math., 75 (1978), 137-147.
  • L. Kronecker, Grundz¨uge einer arithmetischen Theorie der algebraischen Gr¨ossen, J. Reine Angew. Math., 92 (1882), 1-122.
  • W. Krull, Beitr¨age zur Arithmetik kommutativer Integrit¨atesbereiche, Math. Zeit., 41 (1936), 545-577.
  • R. Matsuda, Note on the number of semistar-operations, Math. J. Ibaraki Univ., 31 (1999), 47-53.
  • R. Matsuda, Note on the number of semistar operations, VIII, Math. J. Ibaraki Univ., 37 (2005), 53-79.
  • R. Matsuda, Commutative Semigroup Rings, 2nd. ed., Kaisei, Tokyo, 2006.
  • R. Matsuda, Semistar operations on pseudo-valuation domains, JP J. Algebra Number Theory Appl., 17 (2010), 163-172. Ryˆuki Matsuda 42 Hori, Mito, Ibaraki 310-0903, JAPAN e-mail: rmazda@adagio.ocn.ne.jp
Year 2011, Volume: 10 Issue: 10, 37 - 55, 01.12.2011

Abstract

References

  • A. Badawi and E. Houston, Powerful ideals, strongly primary ideals, almost pseudo-valuation domains, and conducive domains, Comm. Alg., 30 (2002), 1606.
  • M. Fontana and K. Loper, Kronecker function rings: a general approach, Ideal Theoretic Methods in Commutative Algebra, Lecture Notes in Pure and Appl. Math., 220, M. Dekker, New York, 2001, 189-205.
  • M. Fontana and K. Loper, An historical overview of Kronecker function rings, Nagata rings, and related star and semistar operations, Multiplicative Ideal Theory in Commutative Algebra, Springer, New York, 2006, 169-187.
  • R. Gilmer, Multiplicative Ideal Theory, M. Dekker, New York, 1972.
  • F. Halter-Koch, Ideal Systems: An Introduction to Multiplicative Ideal The- ory, M. Dekker, New York, 1998.
  • J. Hedstrom and E. Houston, Pseudo-valuation domains, PaciŞc J. Math., 75 (1978), 137-147.
  • L. Kronecker, Grundz¨uge einer arithmetischen Theorie der algebraischen Gr¨ossen, J. Reine Angew. Math., 92 (1882), 1-122.
  • W. Krull, Beitr¨age zur Arithmetik kommutativer Integrit¨atesbereiche, Math. Zeit., 41 (1936), 545-577.
  • R. Matsuda, Note on the number of semistar-operations, Math. J. Ibaraki Univ., 31 (1999), 47-53.
  • R. Matsuda, Note on the number of semistar operations, VIII, Math. J. Ibaraki Univ., 37 (2005), 53-79.
  • R. Matsuda, Commutative Semigroup Rings, 2nd. ed., Kaisei, Tokyo, 2006.
  • R. Matsuda, Semistar operations on pseudo-valuation domains, JP J. Algebra Number Theory Appl., 17 (2010), 163-172. Ryˆuki Matsuda 42 Hori, Mito, Ibaraki 310-0903, JAPAN e-mail: rmazda@adagio.ocn.ne.jp
There are 12 citations in total.

Details

Other ID JA98AN63HZ
Journal Section Articles
Authors

Ryûki Matsuda This is me

Publication Date December 1, 2011
Published in Issue Year 2011 Volume: 10 Issue: 10

Cite

APA Matsuda, R. (2011). SEMISTAR OPERATIONS ON ALMOST PSEUDO-VALUATION DOMAINS. International Electronic Journal of Algebra, 10(10), 37-55.
AMA Matsuda R. SEMISTAR OPERATIONS ON ALMOST PSEUDO-VALUATION DOMAINS. IEJA. December 2011;10(10):37-55.
Chicago Matsuda, Ryûki. “SEMISTAR OPERATIONS ON ALMOST PSEUDO-VALUATION DOMAINS”. International Electronic Journal of Algebra 10, no. 10 (December 2011): 37-55.
EndNote Matsuda R (December 1, 2011) SEMISTAR OPERATIONS ON ALMOST PSEUDO-VALUATION DOMAINS. International Electronic Journal of Algebra 10 10 37–55.
IEEE R. Matsuda, “SEMISTAR OPERATIONS ON ALMOST PSEUDO-VALUATION DOMAINS”, IEJA, vol. 10, no. 10, pp. 37–55, 2011.
ISNAD Matsuda, Ryûki. “SEMISTAR OPERATIONS ON ALMOST PSEUDO-VALUATION DOMAINS”. International Electronic Journal of Algebra 10/10 (December 2011), 37-55.
JAMA Matsuda R. SEMISTAR OPERATIONS ON ALMOST PSEUDO-VALUATION DOMAINS. IEJA. 2011;10:37–55.
MLA Matsuda, Ryûki. “SEMISTAR OPERATIONS ON ALMOST PSEUDO-VALUATION DOMAINS”. International Electronic Journal of Algebra, vol. 10, no. 10, 2011, pp. 37-55.
Vancouver Matsuda R. SEMISTAR OPERATIONS ON ALMOST PSEUDO-VALUATION DOMAINS. IEJA. 2011;10(10):37-55.