INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY

Mangesh B. Rege; Ardeline Mary Buhphang

INTEGRALLY CLOSED RINGS AND THE ARMENDARIZ PROPERTY

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

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.