Abstract
Previously the following question was offered by Zariski [6]:Is any normal Noetherian local ring analytically irreducible?In the present note, we will construct a counter-example against the question.TERMINOLOGY. A ring (integrity domain) means always a commutative ring (integrity domain) with identity. A normal ring is an integrity domain which is integrally closed in its field of quotients. When 0 is an integrity domain, the integral closure of 0 in its field of quotients is called the derived normal ring of 0.
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