Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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INTEGRAL DOMAINS WITH FINITELY MANY STAR OPERATIONS OF FINITE TYPE

  • Received : 2012.04.07
  • Accepted : 2012.06.10
  • Published : 2012.06.30
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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 ${\mid}SF(D){\mid}{\leq}2$.

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References

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