On root closure in commutative rings

Arabian Journal for Science and Engineering

Volumn 26, Issue 1 C, 2001, Pages 17-30

  Anderson, David F ^a   Badawi, Ayman ^b  

^a UNIVERSITY OF TENNESSEE   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035536174     PISSN: 2193567X     EISSN: 21914281     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. D.F. Anderson, "Root Closure in Integral Domains", J. Algebra, 79 (1982), pp. 51-59.
2. R.G. Swan, "On Seminormality", J. Algebra, 67 (1980), pp. 210-229.
3. D.E. Rush, "Seminormality", J. Algebra, 67 (1980), pp. 377-384.
4. R. Gilmer and R.C. Heitmann, "On Pic(R[X]) for R Seminormal", J. Pure Appl. Algebra, 16 (1980), pp. 251-257.
5. D.F. Anderson and A. Badawi, "Conditions Equivalent to Seminormality in Certain Classes of Commutative Rings", Lecture Notes in Pure and Applied Mathematics, 220 (2001), pp. 49-59. New York/Basel: Marcel Dekker.
6. A. Badawi, D.F. Anderson, and D.E. Dobbs, "Pseudo-Valuation Rings", Lecture Notes in Pure and Applied Mathematics, 185, (1997), pp. 57-67. New York/Basel: Marcel Dekker.
7. D.F. Anderson, A. Badawi, and D.E. Dobbs, "Pseudo-Valuation Rings, II", Boll. Un. Mat. Ital., B(8) 3 (2000), pp. 535-545.
8. A. Badawi, "On Domains Which Have Prime Ideals That are Linearly Ordered", Comm. Algebra, 23 (1995), pp. 4365-4373.
9. A. Badawi, "On Φ-Pseudo-Valuation Rings", Lecture Notes in Pure and Applied Mathematics, 205 (1999), pp. 101-110. New York/Basel: Marcel Dekker.
10. D.D. Anderson and D.F. Anderson, "Multiplicatively Closed Subsets of Fields", Houston J. Math., 13 (1987), pp. 1-11.
11. J. Sato and T. Sugatani, "On the Radical Ideals of Seminormal Rings", Comm. Algebra, 18 (1990), pp. 441-451.
12. D.F. Anderson and J. Park, "Rooty and Root Closed Domains", Lecture Notes in Pure and Applied Mathematics, 205 (1999), pp. 87-99. New York/Basel: Marcel Dekker.
13. R. Gilmer, Multiplicative Ideal Theory. New York/Basel: Marcel Dekker, 1972.
14. J. Huckaba, Commutative Rings with Zero Divisors. New York/Basel: Marcel Dekker, 1988.
15. I. Kaplansky, Commutative Rings, rev. edn. Chicago: Univ. of Chicago Press, 1974.
16. D.F. Anderson, "Root Closure in Commutative Rings: a Survey", Lecture Notes in Pure and Applied Mathematics, 205 (1999), pp. 55-71. New York/Basel: Marcel Dekker.
17. J.R. Hedstrom and E.G. Houston, "Pseudo-Valuation Domains", Pacific J. Math., 75 (1978), pp. 137-147.
18. A. Badawi, "On Φ-Pseudo-Valuation Rings, II", Houston J. Math., 26 (2000), pp. 473-480.