Pith Number

pith:P6SESCGZ

pith:2023:P6SESCGZIQCVPHQKIRNWMSMDRG

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Notes on modules of finite injective dimension

Mohsen Asgharzadeh

Existence of finitely generated modules of finite injective dimension forces the ring to be reduced, normal, an integral domain, complete intersection or Gorenstein beyond Cohen-Macaulay.

arxiv:2301.01105 v6 · 2023-01-03 · math.AC

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\pithnumber{P6SESCGZIQCVPHQKIRNWMSMDRG}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

The existence of finitely generated modules of finite injective dimension forces the ambient ring to be reduced, normal, an integral domain, complete intersection, or Gorenstein, beyond the Cohen-Macaulay property.

C2weakest assumption

The paper assumes the standard Noetherian commutative ring setting of the Bass conjecture and that the modules under study are finitely generated over that ring; if the ring is not Noetherian or the modules are not finitely generated, the forcing statements on ring properties may fail to hold.

C3one line summary

Finitely generated modules of finite injective dimension over a ring force the ring to satisfy properties including reducedness, normality, being an integral domain, complete intersection, or Gorenstein.

Receipt and verification

First computed	2026-05-26T02:04:58.013441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fa44908d94405579e0a445b664983899a07509ccd5e79be386474fe6245cbfe

Aliases

arxiv: 2301.01105 · arxiv_version: 2301.01105v6 · doi: 10.48550/arxiv.2301.01105 · pith_short_12: P6SESCGZIQCV · pith_short_16: P6SESCGZIQCVPHQK · pith_short_8: P6SESCGZ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/P6SESCGZIQCVPHQKIRNWMSMDRG \
  | 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: 7fa44908d94405579e0a445b664983899a07509ccd5e79be386474fe6245cbfe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57be155bccc5b19205157c00264bf96e9464f28d1cdf62536f7f22e27d85e4bf",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2023-01-03T13:59:12Z",
    "title_canon_sha256": "c5ffb98a8c28d2fb197a73d6d63efa0326d938ebbb5293ef9311dbb911931962"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2301.01105",
    "kind": "arxiv",
    "version": 6
  }
}