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http://dx.doi.org/10.11568/kjm.2012.20.2.185

INTEGRAL DOMAINS WITH FINITELY MANY STAR OPERATIONS OF FINITE TYPE  

Chang, Gyu Whan (Department of Mathematics University of Incheon)
Publication Information
Korean Journal of Mathematics / v.20, no.2, 2012 , pp. 185-191 More about this Journal
Abstract
Let D be an integral domain and SF(D) be the set of star operations of finite type on D. We show that if ${\mid}SF(D){\mid}$ < ${\infty}$, 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 ${\mid}SF(D){\mid}={\infty}$. We also study the integrally closed domains D with ${\mid}SF(D){\mid}{\leq}2$.
Keywords
star operation of finite type; Pr$\ddot{u}$fer domain; pseudo-valuation domain;
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