## A two-dimensional domain whose integral closure is not t-linked.(English)Zbl 1033.13005

Summary: We construct a two-dimensional domain $$D$$ having two nonzero $$v$$-coprime elements $$a$$, $$b$$ such that $$a$$ and $$b$$ are not $$v$$-coprime in the integral closure of $$D$$.

### MSC:

 13G05 Integral domains 13B22 Integral closure of commutative rings and ideals 13A18 Valuations and their generalizations for commutative rings

### Keywords:

integral closure; $$t$$-linked overring; $$v$$-coprime
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