Connecting Trace Properties
The study of commutative integral domains often involves the interplay between special collections of ideals and overrings. Structural properties are identified, analyzed, and classified by using the techniques and results of ideal theory. Gilmer’s 1972 book, Multiplicative Ideal Theory, serves as an excellent introduction and foundation to this perspective [G], and the recent book of Fontana, Huckaba, and Papick, Prüfer Domains, continues in this spirit [FHP].
KeywordsPrime Ideal Maximal Ideal Trace Ideal Minimal Prime Ideal Dedekind Domain
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- [CL]P.-J. Cahen and T. Lucas, The special trace property, Commutative Ring Theory: Proceedings of the II International Conference, Marcel Dekker, New York, 1997, 161–172.Google Scholar
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- [KLM 2]S. Kabbaj, T. Lucas and A. Mimouni, Trace properties and pullbacks, I, preprint.Google Scholar
- [LM]T. Lucas and A. Mimouni, Trace properties and pullbacks, II, preprint.Google Scholar