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INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY

Year 2007, Volume: 1 Issue: 1, 11 - 17, 01.06.2007

Mangesh B. Rege Ardeline Mary Buhphang

Abstract

Armendariz rings are defined through polynomial rings over them.
Polynomial rings over Armendariz rings are known to be Armendariz; we show
that power series rings need not be so.

Keywords

Armendariz ring Armendariz module integrally closed ring

References

  • D.D. Anderson and V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra, 26(7) (1998), 2265-2272.
  • E.P. Armendariz, A note on extensions of Baer and pp-rings, J.Australian Math.Soc., 18 (1974), 470-473.
  • N. Bourbaki, Elements of Mathematics, Commutative Algebra, Addison- Wesley, 1972.
  • J.W. Brewer, Power Series over Commutative Rings, Marcel Dekker, New York, 1981.
  • A.M. Buhphang and M.B. Rege, Semi-commutative modules and Armendariz modules, Arab J.Math.Sc., 8 (2002), 53-65.
  • R. Gilmer, A note on the quotient field of the domain D[[X]], Proc. Amer.Math.Soc., 18 (1967), 1138-1140.
  • R. Gilmer, Multiplicative Ideal Theory, Marcel Dekker, New York, 1972. Guo Ying, Du Xian-kun, Xie Jing-ran,
  • Armendariz rings and skew Armendariz rings, Journal of Jilin University (2005),

Year 2007, Volume: 1 Issue: 1, 11 - 17, 01.06.2007

Mangesh B. Rege Ardeline Mary Buhphang

Abstract

References

  • D.D. Anderson and V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra, 26(7) (1998), 2265-2272.
  • E.P. Armendariz, A note on extensions of Baer and pp-rings, J.Australian Math.Soc., 18 (1974), 470-473.
  • N. Bourbaki, Elements of Mathematics, Commutative Algebra, Addison- Wesley, 1972.
  • J.W. Brewer, Power Series over Commutative Rings, Marcel Dekker, New York, 1981.
  • A.M. Buhphang and M.B. Rege, Semi-commutative modules and Armendariz modules, Arab J.Math.Sc., 8 (2002), 53-65.
  • R. Gilmer, A note on the quotient field of the domain D[[X]], Proc. Amer.Math.Soc., 18 (1967), 1138-1140.
  • R. Gilmer, Multiplicative Ideal Theory, Marcel Dekker, New York, 1972. Guo Ying, Du Xian-kun, Xie Jing-ran,
  • Armendariz rings and skew Armendariz rings, Journal of Jilin University (2005),
There are 8 citations in total.

Details

Other ID JA25GM89NN
Journal Section Articles
Authors

Mangesh B. Rege This is me

Ardeline Mary Buhphang This is me

Publication Date June 1, 2007
Published in Issue Year 2007 Volume: 1 Issue: 1

Cite

APA Rege, M. B., & Buhphang, A. M. (2007). INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY. International Electronic Journal of Algebra, 1(1), 11-17.
AMA Rege MB, Buhphang AM. INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY. IEJA. June 2007;1(1):11-17.
Chicago Rege, Mangesh B., and Ardeline Mary Buhphang. “INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY”. International Electronic Journal of Algebra 1, no. 1 (June 2007): 11-17.
EndNote Rege MB, Buhphang AM (June 1, 2007) INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY. International Electronic Journal of Algebra 1 1 11–17.
IEEE M. B. Rege and A. M. Buhphang, “INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY”, IEJA, vol. 1, no. 1, pp. 11–17, 2007.
ISNAD Rege, Mangesh B. - Buhphang, Ardeline Mary. “INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY”. International Electronic Journal of Algebra 1/1 (June 2007), 11-17.
JAMA Rege MB, Buhphang AM. INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY. IEJA. 2007;1:11–17.
MLA Rege, Mangesh B. and Ardeline Mary Buhphang. “INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY”. International Electronic Journal of Algebra, vol. 1, no. 1, 2007, pp. 11-17.
Vancouver Rege MB, Buhphang AM. INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY. IEJA. 2007;1(1):11-7.