Geodesic
Crossed group rings of finite groups and rings of $p$-adic integers with finitely many indecomposable integral representations
Sbornik. Mathematics, Tome 36 (1980) no. 2, pp. 173-194 
L. F. Barannik; P. M. Gudivok. Crossed group rings of finite groups and rings of $p$-adic integers with finitely many indecomposable integral representations. Sbornik. Mathematics, Tome 36 (1980) no. 2, pp. 173-194. http://geodesic.mathdoc.fr/item/SM_1980_36_2_a2/
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     title = {Crossed group rings of finite groups and rings of $p$-adic integers with finitely many indecomposable integral representations},
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     volume = {36},
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     url = {http://geodesic.mathdoc.fr/item/SM_1980_36_2_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $F$ be a finite extension of the field $Q_p$ of rational $p$-adic numbers, $R$ the ring of all integral elements of $F$, $ R^*$ the multiplicative group of $R$, $G$ a finite group, and $\Lambda=(G,R,\lambda)$ the crossed group ring of $G$ and $R$ with the factor system $\{\lambda_{a,b}\}$ ($\lambda_{a,b}\in R^*$; $a,b\in G$). A classification is given of the rings $\Lambda$ for which the number of indecomposable $R$-representations is finite. When $\Lambda$ is a group ring, this problem was solved in papers by Faddeev, Borevich, Gudivok, Yakobinskii, and others. Bibliography: 22 titles.

[1] 3. I. Borevich, D. K. Faddeev, “Teoriya gomologii v gruppakh. II”, Vestnik LGU, 1959, no. 7, 72–87 | Zbl

[2] S. D. Berman i P. M. Gudivok, “O tselochislennykh predstavleniyakh konechnykh grupp”, DAN SSSR, 145:6 (1962), 1190–1201 | MR

[3] S. D. Berman i P. M. Gudivok, “Nerazlozhimye predstavleniya konechnykh grupp nad koltsom tselykh $p$-adicheskikh chisel”, Izv. AN SSSR, seriya matem., 28:4 (1964), 875–910 | MR | Zbl

[4] A. Heller, I. Reiner, “On groups with finitely many indecomposable integral representations”, Bull. Amer. Math. Soc., 68:3 (1962), 210–212 | DOI | MR | Zbl

[5] A. Heller, I. Reiner, “Representations of cyclic groups in rings of integers. I; II”, Ann. Math., 76 (1962), 73–92 ; 77 (1963), 318–328 | DOI | MR | Zbl | DOI | MR | Zbl

[6] P. M. Gudivok, “Predstavleniya konechnykh grupp nad chislovymi koltsami”, Izv. AN SSSR, seriya matem., 31 (1967), 799–834 | MR | Zbl

[7] H. Yacobinski, “Sur les ordres commutatifs avec un nombre fini de reseaux indecomposables”, Acta Math., 118 (1967), 1–31 | DOI | MR

[8] P. M. Gudivok, “O chisle nerazlozhimykh tselochislennykh $p$-adicheskikh predstavlenii skreschennykh gruppovykh kolets”, Matem. sb., 91(133) (1973), 27–49 | MR | Zbl

[9] Yu. A. Drozd, A. V. Roiter, “Kommutativnye koltsa s konechnym chislom tselochislennykh nerazlozhimykh predstavlenii”, Izv. AN SSSR, seriya matem., 31 (1967), 783–798 | MR | Zbl

[10] Yu. A. Drozd, V. V. Kirichenko, “Primarnye poryadki s konechnym chislom nerazlozhimykh predstavlenii”, Izv. AN SSSR, seriya matem., 37 (1973), 715–736 | MR | Zbl

[11] K. W. Roggenkamp, “Classification of the completely primary totally ramified orders with a finite number of nonisomorfic indecomposable lattices”, Bull. Amer. Math. Soc., 78 (1972), 399–401 | DOI | MR | Zbl

[12] L. F. Barannik, P. M. Gudivok, “O chisle nerazlozhimykh tselochislennykh predstavlenii skreschennykh gruppovykh kolets konechnykh grupp i kolets tselykh r-adicheskikh chisel”, Matem. sb. AN USSR, Kiev, 1976, 164–167 | MR

[13] Yu. A. Drozd, V. V. Kirichenko, A. V. Roiter, “O nasledstvennykh i bassovykh poryadkakh”, Izv. AN SSSR, seriya matem., 31 (1967), 1415–1436 | MR | Zbl

[14] Yu. A. Drozd, V. V. Kirichenko, “O kvazibassovykh poryadkakh”, Izv. AN SSSR, seriya matem., 36 (1972), 328–370 | MR | Zbl

[15] Yu. A. Drozd, “Nerazlozhimye matrichnye koltsa vtorogo poryadka s konechnym chislom predstavlenii bassovy”, Matem. zametki, 12:5 (1972), 601–604 | MR | Zbl

[16] Yu. A. Drozd, “Uzagalnennya odniei teoremi Deida”, DAN URSR, seriya A, 1974, no. 3, 204–207 | Zbl

[17] D. K. Faddeev, “Vvedenie v multiplikativnuyu teoriyu modulei tselochislennykh predstavlenii”, Trudy Matem. in-ta im. V. A. Steklova AN SSSR, LXXX, 1965, 145–182 | MR

[18] 3. I. Borevich, I. R. Shafarevich, Teoriya chisel, izd-vo “Nauka”, Moskva, 1964

[19] A. A. Albert, Structure of algebras, New York, 1939

[20] S. Leng, Algebra, izd-vo “Mir”, Moskva, 1968

[21] L. F. Barannik, P. M. Gudivok, “Proektivnye predstavleniya konechnykh grupp nad chislovymi koltsami”, Matem. sb., 82(124) (1970), 423–443 | MR | Zbl

[22] M. Kholl, Teoriya grupp, IL, Moskva, 1962