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Integral domains with finitely many star operations of finite type
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Let D be an integral domain and SF(D) be the set of star operations of nite type on D. We show that if |SF(D)| < ∞,then every maximal ideal of D is a t-ideal. We give an example of integrally closed quasi-local domains D in which the maximal ideal is divisorial (so a t-ideal) but |SF(D)| = ∞. We also study the integrally closed domains D with |SF(D)| ≤ 2.
Abstract
Let D be an integral domain and SF(D) be the set of star operations of nite type on D. We show that if |SF(D)| < ∞,then every maximal ideal of D is a t-ideal. We give an example of integrally closed quasi-local domains D in which the maximal ideal is divisorial (so a t-ideal) but |SF(D)| = ∞. We also study the integrally closed domains D with |SF(D)| ≤ 2.
참고문헌 (13)
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- E. Houston, "Integral domains which admit at most two star operations", Comm. Algebra, 39, pp.1907~1921 (2011)
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