Pith Number

pith:U2DYLBJN

pith:2026:U2DYLBJNCRQQ4YYGX3NE2W4XRG

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Separable functors and firm modules

Patrik Lundstr\"om

Firm modules over nonunital rings support separable functors and a locally unital Maschke theorem for group rings.

arxiv:2602.13417 v2 · 2026-02-13 · math.RA · math.RT

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Record completeness

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4 Citations open

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Claims

C1strongest claim

We prove nonunital analogues of classical results on functorial separability and semisimplicity, and apply these results to obtain a locally unital version of Maschke's theorem for group rings.

C2weakest assumption

That the category of firm modules over a nonunital ring supplies a sufficiently rich and well-behaved setting in which the classical notions of separability and semisimplicity can be defined and proved without additional hidden restrictions.

C3one line summary

Develops nonunital analogues of functorial separability and semisimplicity for firm modules and applies them to a locally unital Maschke theorem for group rings.

References

26 extracted · 26 resolved · 0 Pith anchors

[1] P. N. ´Anh and L. M´ arki, Morita equivalence for rings without identity, Tsukuba J. Math.11(1987), 1–16 1987

[2] Baer, Absolute retracts in group theory, Bull 1946

[3] G. B¨ ohm and J. G´ omez-Torrecillas, Firm monads and firm Frobenius algebras, Bull. Math. Soc. Sci. Math. Roumanie56(2013), 281–298 2013

[4] T. Brzezi´ nski, L. Kadison and R. Wisbauer, On coseparable and biseparable corings, in:Hopf Algebras in Noncommutative Geometry and Physics, Pure Appl. Math., vol. 239, Marcel Dekker, New York, 2005 2005

[5] J. Cala, P. Lundstr¨ om and H. Pinedo, Object-unital groupoid graded rings, crossed products and separability, Comm. Algebra49(2021), 1676–1696 2021

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Separability for relative extensions of object unital strongly groupoid graded rings

Receipt and verification

First computed	2026-05-18T03:09:23.545544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a68785852d14610e6306beda4d5b9789b2e2a9ac0e8f9e031edd9a2334347b38

Aliases

arxiv: 2602.13417 · arxiv_version: 2602.13417v2 · doi: 10.48550/arxiv.2602.13417 · pith_short_12: U2DYLBJNCRQQ · pith_short_16: U2DYLBJNCRQQ4YYG · pith_short_8: U2DYLBJN

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/U2DYLBJNCRQQ4YYGX3NE2W4XRG \
  | 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: a68785852d14610e6306beda4d5b9789b2e2a9ac0e8f9e031edd9a2334347b38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75931a8509446a6089bd99190ce00d7cb2b3b406d102485d7ff11bc7d367f89b",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2026-02-13T19:37:52Z",
    "title_canon_sha256": "639b0c4e1a1febb0bda2082ba8584d4bc904f01f9f5392f6270cf230990381ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.13417",
    "kind": "arxiv",
    "version": 2
  }
}