Relative injective modules, superstability and noetherian
categories

J 2026

Relative injective modules, superstability and noetherian categories

MAZARI-ARMIDA, Marcos a Jiří ROSICKÝ

Základní údaje

Originální název

Relative injective modules, superstability and noetherian categories

Autoři

MAZARI-ARMIDA, Marcos a Jiří ROSICKÝ

Vydání

JOURNAL OF MATHEMATICAL LOGIC, SINGAPORE, WORLD SCIENTIFIC PUBL CO PTE LTD, 2026, 0219-0613

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Singapur

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.900 v roce 2024

Označené pro přenos do RIV

Ano

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Relative injective modules; Baer criterion; stable independence relation; superstability; noetherian categories; abstract elementary classes

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 24. 4. 2026 09:23, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

We study classes of modules closed under direct sums, M-submodules and M-epimorphic images where M is either the class of embeddings, RD-embeddings or pure embeddings. We show that the M-injective modules of theses classes satisfy a Baer-like criterion. In particular, injective modules, RD-injective modules, pure injective modules, flat cotorsion modules and s-torsion pure injective modules satisfy this criterion. The argument presented is a model theoretic one. We use in an essential way stable independence relations which generalize Shelah's non-forking to abstract elementary classes. We show that the classical model theoretic notion of superstability is equivalent to the algebraic notion of a noetherian category for these classes. We use this equivalence to characterize noetherian rings, pure semisimple rings, perfect rings and finite products of finite rings and artinian valuation rings via superstability.

Návaznosti

GA22-02964S, projekt VaV

Název: Obohacené kategorie a jejich aplikace (Akronym: ECATA)

Investor: Grantová agentura ČR, Enriched categories and their applications

Citovat

MAZARI-ARMIDA, Marcos a Jiří ROSICKÝ. Relative injective modules, superstability and noetherian categories. JOURNAL OF MATHEMATICAL LOGIC. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD, 2026, roč. 26, č. 01, s. 1-32. ISSN 0219-0613. Dostupné z: https://doi.org/10.1142/S0219061324500272.

@article{2568258,
   author = {MazariandArmida, Marcos and Rosický, Jiří},
   article_location = {SINGAPORE},
   article_number = {01},
   doi = {https://doi.org/10.1142/S0219061324500272},
   keywords = {Relative injective modules; Baer criterion; stable independence relation; superstability; noetherian categories; abstract elementary classes},
   language = {eng},
   issn = {0219-0613},
   journal = {JOURNAL OF MATHEMATICAL LOGIC},
   title = {Relative injective modules, superstability and noetherian categories},
   url = {https://www.worldscientific.com/doi/10.1142/S0219061324500272},
   volume = {26},
   year = {2026}
}

TY  - JOUR
ID  - 2568258
AU  - Mazari-Armida, Marcos - Rosický, Jiří
PY  - 2026
TI  - Relative injective modules, superstability and noetherian categories
JF  - JOURNAL OF MATHEMATICAL LOGIC
VL  - 26
IS  - 01
SP  - 1-32
EP  - 1-32
PB  - WORLD SCIENTIFIC PUBL CO PTE LTD
SN  - 02190613
KW  - Relative injective modules
KW  - Baer criterion
KW  - stable independence relation
KW  - superstability
KW  - noetherian categories
KW  - abstract elementary classes
UR  - https://www.worldscientific.com/doi/10.1142/S0219061324500272
N2  - We study classes of modules closed under direct sums, M-submodules and M-epimorphic images where M is either the class of embeddings, RD-embeddings or pure embeddings. We show that the M-injective modules of theses classes satisfy a Baer-like criterion. In particular, injective modules, RD-injective modules, pure injective modules, flat cotorsion modules and s-torsion pure injective modules satisfy this criterion. The argument presented is a model theoretic one. We use in an essential way stable independence relations which generalize Shelah's non-forking to abstract elementary classes. We show that the classical model theoretic notion of superstability is equivalent to the algebraic notion of a noetherian category for these classes. We use this equivalence to characterize noetherian rings, pure semisimple rings, perfect rings and finite products of finite rings and artinian valuation rings via superstability.
ER  -

MAZARI-ARMIDA, Marcos a Jiří ROSICKÝ. Relative injective modules, superstability and noetherian categories. \textit{JOURNAL OF MATHEMATICAL LOGIC}. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD, 2026, roč.~26, č.~01, s.~1-32. ISSN~0219-0613. Dostupné z: https://doi.org/10.1142/S0219061324500272.

Přehled o publikaci