How Long Is 5 Billion Light Years Deepleeqe Not quite since there could be a unique minimal prime mathfrak p and some other prime ideal mathfrak q not containing mathfrak p as a prime need not contain a
Dec 30 2011 nbsp 0183 32 Yes indeed The minimal prime ideals containing I I and the minimal associated primes of I I coincide You may find this result in Atiyah s commutative algebra Is there a quot general approach quot to determine the minimal prime ideals over an ideal J J I checked some books and didn t find a general approach Maybe the theory of Gr 246 bner bases is related
How Long Is 5 Billion Light Years
How Long Is 5 Billion Light Years
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Jun 9 2011 nbsp 0183 32 The non zero elements of the minimal prime ideals of a noetherian commutative ring are zero divisors The proof of this fact I know of uses primary decomposition
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How Long Is 5 Billion Light Years

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Jul 7 2016 nbsp 0183 32 From Wikipedia A prime ideal P is said to be a minimal prime ideal over an ideal I if it is minimal among all prime ideals containing I Note that we do not exclude I even if it is a

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Dear Akhil No I think you are okay A P has a unique maximal ideal which is also a minimal prime and hence has a unique minimal prime too PA P is simultaneously uniquely maximal

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Mar 18 2023 nbsp 0183 32 Minimal prime ideals are generic points of irreducible components Has your course covered generic points yet

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Mar 28 2016 nbsp 0183 32 Show that under this bijection prime ideals are in bijective correspondence with irreducible closed sets In particular minimal prime ideals correspond to maximal irreducible sets

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Mar 17 2018 nbsp 0183 32 Berci In this context the OP presumably means truly minimal so for an integral domain the zero ideal would be the unique minimal prime ideal Otherwise if quot minimal prime
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