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pith:5QBE6CTD

pith:2025:5QBE6CTDNMXUHD6EXTFB5S3SHA

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Equivalence classes of Wakamatsu tilting modules and preenveloping and precovering subcategories

Ali Mahin Fallah, Kamran Divaani-Aazar, Massoud Tousi

An equivalence relation on Wakamatsu tilting modules extends the Mantese-Reiten theorems to arbitrary associative rings.

arxiv:2512.11600 v2 · 2025-12-12 · math.RT

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Claims

C1strongest claim

We introduce an equivalence relation on the class of Wakamatsu tilting right R modules. By using this equivalence relation, we extend the Mantese Reiten theorems from the setting of Artin algebras to that of arbitrary associative rings.

C2weakest assumption

The introduced equivalence relation on Wakamatsu tilting modules preserves the properties needed for the Mantese-Reiten theorems to hold without extra conditions on the arbitrary associative ring R.

C3one line summary

An equivalence relation on Wakamatsu tilting modules extends Mantese-Reiten theorems from Artin algebras to arbitrary associative rings.

References

28 extracted · 28 resolved · 0 Pith anchors

[1] F. W. Anderson and K. R. Fuller,Rings and categories of modules, (2nd ed.), Graduate Texts in Mathematics, 13, New York, Springer-Verlag, (1992) 1992

[2] Angeleri H¨ ugel,Infinite dimensional tilting theory, Advances in representation theory of algebras, EMS Series of Congress Reports, Z¨ urich, (2013), 1–37 2013

[3] Angeleri H¨ ugel,Finitely cotilting modules, Commun 2000

[4] I. Assem, D. Simson and A. Skowro´ nski,Elements of the representation theory of associative algebras, vol. 1: Techniques of representation theory, London Mathematical Society Student Texts,65, Cambri 2006

[5] Auslander,Functors and morphisms determined by objects, Represent 1978

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Receipt and verification

First computed	2026-05-18T03:10:11.550705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec024f0a636b2f438fc4bcca1ecb72382c3ecaa9aa2cf1d5bc8f2ae3ca124ea5

Aliases

arxiv: 2512.11600 · arxiv_version: 2512.11600v2 · doi: 10.48550/arxiv.2512.11600 · pith_short_12: 5QBE6CTDNMXU · pith_short_16: 5QBE6CTDNMXUHD6E · pith_short_8: 5QBE6CTD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5QBE6CTDNMXUHD6EXTFB5S3SHA \
  | 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: ec024f0a636b2f438fc4bcca1ecb72382c3ecaa9aa2cf1d5bc8f2ae3ca124ea5

Canonical record JSON

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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2025-12-12T14:35:19Z",
    "title_canon_sha256": "5ba4d60ea55623875f0674b194c2e52e944512db1d95dbe2c724eb78226c15cc"
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