Browse > Article
http://dx.doi.org/10.4134/BKMS.b210322

TRACE PROPERTIES AND INTEGRAL DOMAINS, III  

Lucas, Thomas G. (Department of Mathematics and Statistics University of North Carolina Charlotte)
Mimouni, Abdeslam (Department of Mathematics King Fahd University of Petroleum and Minerals)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.2, 2022 , pp. 419-429 More about this Journal
Abstract
An integral domain R is an RTP domain (or has the radical trace property) (resp. an LTP domain) if I(R : I) is a radical ideal for each nonzero noninvertible ideal I (resp. I(R : I)RP = PRP for each minimal prime P of I(R : I)). Clearly each RTP domain is an LTP domain, but whether the two are equivalent is open except in certain special cases. In this paper, we study the descent of these notions from particular overrings of R to R itself.
Keywords
Trace ideal; radical trace property; RTP domain; LTP domain;
Citations & Related Records
연도 인용수 순위
  • Reference
1 D. D. Anderson, J. A. Huckaba, and I. J. Papick, A note on stable domains, Houston J. Math. 13 (1987), no. 1, 13-17.
2 H. Bass, On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8-28. https://doi.org/10.1007/BF01112819   DOI
3 S. Bazzoni and L. Salce, Warfield domains, J. Algebra 185 (1996), no. 3, 836-868. https://doi.org/10.1006/jabr.1996.0353   DOI
4 M. Fontana, E. Houston, and T. Lucas, Factoring ideals in integral domains, Lecture Notes of the Unione Matematica Italiana, 14, Springer, Heidelberg, 2013. https://doi. org/10.1007/978-3-642-31712-5   DOI
5 M. Fontana, J. A. Huckaba, and I. J. Papick, Domains satisfying the trace property, J. Algebra 107 (1987), no. 1, 169-182. https://doi.org/10.1016/0021-8693(87)90083-4   DOI
6 W. J. Heinzer and I. J. Papick, The radical trace property, J. Algebra 112 (1988), no. 1, 110-121. https://doi.org/10.1016/0021-8693(88)90135-4   DOI
7 S.-E. Kabbaj, T. G. Lucas, and A. Mimouni, Trace properties and integral domains, in Advances in commutative ring theory (Fez, 1997), 421-436, Lecture Notes in Pure and Appl. Math., 205, Dekker, New York, 1999.
8 T. G. Lucas and D. McNair, Trace properties in rings with zero divisors, J. Algebra 343 (2011), 201-223. https://doi.org/10.1016/j.jalgebra.2011.05.039   DOI
9 P. Jaffard, Th'eorie arithm'etique des anneaux du type de Dedekind, Bull. Soc. Math. France 80 (1952), 61-100.   DOI
10 E. G. Houston, S. Kabbaj, T. G. Lucas, and A. Mimouni, When is the dual of an ideal a ring?, J. Algebra 225 (2000), no. 1, 429-450. https://doi.org/10.1006/jabr.1999.8142   DOI
11 S.-E. Kabbaj, T. G. Lucas, and A. Mimouni, Trace properties and pullbacks, Comm. Algebra 31 (2003), no. 3, 1085-1111. https://doi.org/10.1081/AGB-120017753   DOI
12 T. G. Lucas, The radical trace property and primary ideals, J. Algebra 184 (1996), no. 3, 1093-1112. https://doi.org/10.1006/jabr.1996.0301   DOI
13 T. G. Lucas and A. Mimouni, Trace properties and the rings R(x) and Rhxi, Ann. Mat. Pura Appl. (4) 199 (2020), no. 5, 2087-2104. https://doi.org/10.1007/s10231-020-00957-8   DOI
14 E. Matlis, Cotorsion modules, Mem. Amer. Math. Soc. 49 (1964), 66 pp.