Pith Number

pith:6F4SZGJM

pith:2026:6F4SZGJMTSKMF7FSCBOBROQOSG

not attested not anchored not stored refs pending

An Integrally Closed Reduced Ring with McCoy Localizations That Is Neither McCoy nor Locally a Domain

Haotian Ma

There exists a reduced and integrally closed commutative ring whose localizations at all maximal ideals are McCoy rings, but the ring itself is neither McCoy nor locally a domain.

arxiv:2604.07465 v2 · 2026-04-08 · math.AC

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We construct an explicit commutative ring R that is reduced and integrally closed, such that R_p is an integrally closed McCoy ring for every maximal ideal p of R, while R itself is not a McCoy ring and is not locally a domain.

C2weakest assumption

That the direct product of Akiba's Nagata-type example and the chosen local integrally closed McCoy ring that is not a domain preserves the local McCoy property at all maximal ideals while retaining the global failure of the McCoy condition.

C3one line summary

Constructs a reduced integrally closed ring with McCoy localizations at maximal ideals but which is not McCoy and not locally a domain.

Receipt and verification

First computed	2026-05-28T02:04:47.371642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1792c992c9c94c2fcb2105c18ba0e91bc5d90a2cafdd96a2d50b6a5a89bf1ed

Aliases

arxiv: 2604.07465 · arxiv_version: 2604.07465v2 · doi: 10.48550/arxiv.2604.07465 · pith_short_12: 6F4SZGJMTSKM · pith_short_16: 6F4SZGJMTSKMF7FS · pith_short_8: 6F4SZGJM

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6F4SZGJMTSKMF7FSCBOBROQOSG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f1792c992c9c94c2fcb2105c18ba0e91bc5d90a2cafdd96a2d50b6a5a89bf1ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66662ea7ca194d1124d7ea14317ddd05d9e7dd7f586a543e2a1a293c5f446049",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-04-08T18:04:13Z",
    "title_canon_sha256": "a20da02a7b87dedf5975477564367c556f157d22afba6299c0a2c309646b1f55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.07465",
    "kind": "arxiv",
    "version": 2
  }
}