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A necessary and sufficient condition for orders in direct sums of complete skewfields to have only finitely many nonisomorphic indecomposable integral representations
Author:
K. W. Roggenkamp
Journal:
Bull. Amer. Math. Soc. 76 (1970), 130-134
MathSciNet review:
0284466
Full-text PDF
References |
Additional Information
- 1.
E.
C. Dade, Some indecomposable group representations, Ann. of
Math. (2) 77 (1963), 406–412. MR 0144981
(26 #2521)
- 2.
Ju.
A. Drozd and A.
V. Roĭter, Commutative rings with a finite number of
indecomposable integral representations, Izv. Akad. Nauk SSSR Ser.
Mat. 31 (1967), 783–798 (Russian). MR 0220716
(36 #3768)
- 3.
Ju.
A. Drozd, V.
V. Kiričenko, and A.
V. Roĭter, Hereditary and Bass orders, Izv. Akad. Nauk
SSSR Ser. Mat. 31 (1967), 1415–1436 (Russian). MR 0219527
(36 #2608)
- 4.
A.
Heller and I.
Reiner, Representations of cyclic groups in rings of integers.
I, Ann. of Math. (2) 76 (1962), 73–92. MR 0140575
(25 #3993)
- 5.
H.
Jacobinski, Sur les ordres commutatifs avec un nombre fini de
réseaux indécomposables, Acta Math. 118
(1967), 1–31 (French). MR 0212001
(35 #2876)
- 6.
K. W. Roggenkamp, Orders in sums of (P-adic skewfields, with an infinite number of integral representations, MS 1968.
- 7.
K. W. Roggenkamp, Charakterisierung von Ordnungen in einer direkten Summe kompletter Schiefkörper, die nur endlich viele nicht isomorphe unzerfällbare Darstellungen haben, Habilitationsarbeit, Gieben, 1969.
- 1.
- E. C. Dade, Some indecomposable group representations, Ann. of Math. (2) 77 (1963), 406-412. MR 144981
- 2.
- Ju. A. Drozd and A. V. Roiter, Commutative rings with a finite number of integral indecomposable representations, Izv. Akad. Nauk SSSR 31 (1967), 783-798. (Russian) MR 220716
- 3.
- Ju. A. Drozd, V. V. Kirichenko and A. V. Roiter, On hereditary orders and Bass orders, Izv. Akad. Nauk SSSR 31 (1967), 1415-1436. (Russian) MR 219527
- 4.
- A. Heller and I. Reiner, Representations of cyclic groups in rings of integers. I, II, Ann of Math. (2) 76 (1962), 73-92; (2) 77 (196), 318-328. MR 140575
- 5.
- H. Jakobinski, Sur les ordres commutatifs avec un nombre fini de réseaux indécomposables, Acta Math. 118 (1967), 1-31. MR 212001
- 6.
- K. W. Roggenkamp, Orders in sums of (P-adic skewfields, with an infinite number of integral representations, MS 1968.
- 7.
- K. W. Roggenkamp, Charakterisierung von Ordnungen in einer direkten Summe kompletter Schiefkörper, die nur endlich viele nicht isomorphe unzerfällbare Darstellungen haben, Habilitationsarbeit, Gieben, 1969.
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1970-12398-9
PII:
S 0002-9904(1970)12398-9
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