$t$-linked overrings as intersections of localizations
HTML articles powered by AMS MathViewer
- by David E. Dobbs, Evan G. Houston, Thomas G. Lucas and Muhammad Zafrullah PDF
- Proc. Amer. Math. Soc. 109 (1990), 637-646 Request permission
Abstract:
This sequel to our work on $t$-linked overrings introduces, characterizes, and applies the $t$-theoretic analogues of integral domains satisfying the $QR$- and $QQR$-properties. In particular, we show that, unlike the situation with $QQR$-domains, the $tQQR$-property is stable under the adjunction of an indeterminate.References
-
D. F. Anderson, E. G. Houston and M. Zafrullah, Pseudo-integrality (submitted for publication).
- Edward D. Davis, Overrings of commutative rings. II. Integrally closed overrings, Trans. Amer. Math. Soc. 110 (1964), 196–212. MR 156868, DOI 10.1090/S0002-9947-1964-0156868-2
- Ada Maria de Souza Doering and Yves Lequain, Chains of prime ideals in polynomial rings, J. Algebra 78 (1982), no. 1, 163–180. MR 677716, DOI 10.1016/0021-8693(82)90106-5
- David E. Dobbs, A characterization of QR-domains, C. R. Math. Rep. Acad. Sci. Canada 11 (1989), no. 2, 49–50. MR 985606
- David E. Dobbs, Evan G. Houston, Thomas G. Lucas, and Muhammad Zafrullah, $t$-linked overrings and Prüfer $v$-multiplication domains, Comm. Algebra 17 (1989), no. 11, 2835–2852. MR 1025612, DOI 10.1080/00927878908823879
- Robert Gilmer, Multiplicative ideal theory, Pure and Applied Mathematics, No. 12, Marcel Dekker, Inc., New York, 1972. MR 0427289
- Robert Gilmer and William J. Heinzer, Intersections of quotient rings of an integral domain, J. Math. Kyoto Univ. 7 (1967), 133–150. MR 223349, DOI 10.1215/kjm/1250524273
- Robert Gilmer and Jack Ohm, Integral domains with quotient overrings, Math. Ann. 153 (1964), 97–103. MR 159835, DOI 10.1007/BF01361178
- Malcolm Griffin, Some results on $v$-multiplication rings, Canadian J. Math. 19 (1967), 710–722. MR 215830, DOI 10.4153/CJM-1967-065-8
- Evan Houston and Muhammad Zafrullah, On $t$-invertibility. II, Comm. Algebra 17 (1989), no. 8, 1955–1969. MR 1013476, DOI 10.1080/00927878908823829
- B. G. Kang, Prüfer $v$-multiplication domains and the ring $R[X]_{N_v}$, J. Algebra 123 (1989), no. 1, 151–170. MR 1000481, DOI 10.1016/0021-8693(89)90040-9
- Joe L. Mott and Muhammad Zafrullah, On Prüfer $v$-multiplication domains, Manuscripta Math. 35 (1981), no. 1-2, 1–26. MR 627923, DOI 10.1007/BF01168446
- Robert L. Pendleton, A characterization of $Q$-domains, Bull. Amer. Math. Soc. 72 (1966), 499–500. MR 190164, DOI 10.1090/S0002-9904-1966-11514-8
- Julien Querré, Sur une propiété des anneaux de Krull, Bull. Sci. Math. (2) 95 (1971), 341–354 (French). MR 299596
- Muhammad Zafrullah, On finite conductor domains, Manuscripta Math. 24 (1978), no. 2, 191–204. MR 485847, DOI 10.1007/BF01310053
- Muhammad Zafrullah, Ascending chain conditions and star operations, Comm. Algebra 17 (1989), no. 6, 1523–1533. MR 997154, DOI 10.1080/00927878908823804
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 637-646
- MSC: Primary 13F05; Secondary 13B30
- DOI: https://doi.org/10.1090/S0002-9939-1990-1017000-7
- MathSciNet review: 1017000