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References
Jones, A.: Groups with a finite number of indecomposable representations. Mich.J.Math. 10 (1963), 257–261.
Jacobinski, H.: Genera and direct decomposition of lattices over orders. J.reine u.angew.Math. 230 (1968), 29–39.
Reiner, I.: Integral representations of cyclic groups of order p2. Proc.Am.Math.Soc. 58 (1976), 8–12.
Drozd, Ju.A.-A.V. Roiter: Commutative rings with a finite number of integral indecomposable representations. Izv.Akad.Nauk S.S.S.R. 31 (1967), 783–798.
Jacobinski, H.: Sur les ordres commutatifs avec un nombre fini de réseaux indécomposable. Acta Math. 118 (1967), 1–31.
Roggenkamp, K.W.: Charakterisierung von Ordnungen in einer direkten Summe kompletter Schiefkörper, die nur endlich viele nicht isomorphe, unzerfällbare Darstellungen haben. Habilitationsschrift, Giessen (1969), 1–122.
Green, E.L.-I. Reiner: Integral representations and diagrams. Mich.J.Math. 25 (1978), 53–84.
Nazarova, L.: Representations of a tetraed. Izv.Akad.Nauk S.S.S.R. 31 (1967), 1361–1378.
Dade, E.C.: Some indecomposable group representations. Ann.of Math. 77 (1963), 406–412.
Roggenkamp, K.W.: Some necessary conditions for orders to be of finite lattice type II. J.reine u.angew.Math. 257 (1972), 12–15.
Riedtmann,Ch.: Algebren, Darstellungsköcher, Überlagerungen und zurück. Comment.Math.Helv.
Wiedemann,A.: Eine Charakterisierung der Gorensteinordnungen durch den Auslander-Reiten Graph. Seminar Univ.Stuttgart (1980).
Roggenkamp,K.W.: Representation theory of finite groups. Presses de l’Université de Montréal, 18e Session Séminaire de Mathématiques Supérieures (1979).
Roggenkamp,K.W.: Representation theory of blocks of defect 1. Proceedings ICRA II, Ottawa (1979).
Diederichsen, E.F.: Über die Ausreduktion ganzzahliger Gruppendarstellungen bei arithmetischer Äquivalenz. Hamb.Abhandlungen 14 (1940), 357–412.
Heller, A.-I. Reiner: Representations of cyclic groups in rings of integers I, II. Ann. of Math. 76 (1962), 73–92, 77 (1963), 318–328.
Higman, D.G.: Induced and produced modules. Can.J.Math. 7 (1955), 490–508.
Bessenroth, Ch.: On blocks of finite lattice type. To appear Archiv d.Math.
Green, J.A.: Vorlesungen über modulare Darstellungstheorie endlicher Gruppen. Vorlesungen aus dem Math, Institut, Univ.Giessen 2 (1974).
Jacobinski,H.: Structure of blocks of defect one. Lecture given at the "International Conference on Representations of Algebras II", Ottawa (1979).
Jakovlev, A.V.: Classification of the 2-adic representations of the cyclic group of order 8. Sem.Leningrad, Inst.Steklov (LOMI) 28 (1972), 93–129.
Hasse, H.: Über p-adische Schiefkörper und ihre Bedeutung für die Arithmetik hyperkomplexer Zahlsysteme. Math.Ann. 104 (1931), 495–534.
Butler, M.C.R.: The 2-adic representations of Klein’s Four Group. Proc. 2nd International Conference in Group Theory, Canberra (1973).
Bäckström,K.J.: Orders with finitely many indecomposable lattices. Ph.D.thesis, Göteborg (1972).
Auslander,M.-S.Ø.Smalø: Preprojective modules over artin algebras. Preprint, Trondheim (1979).
Ringel, C.M.-K.W. Roggenkamp: Diagrammatic methods in the representation theory of orders. To appear J.of Algebra (1980).
Harada, M.: Structure of hereditary orders over local rings. Osaka J.Math. 14 (1963), 1–22.
Brumer, A.: Structure of hereditary orders. Bull.Am.Soc. 69 (1963), 721–729.
Jacobinski, H.: Two remarks on hereditary orders. Proc.Am.Math.Soc. 28 (1971), 1–8.
Auslander, M.-O. Goldman: Maximal orders. Trans.Am.Math.Soc. 97 (1960), 1–24.
Dlab, V.-C.M.Ringel: Indecomposable representations of graphs and algebras. Mem.Am.Math.Soc. 173 Providence (1976).
Auslander, M.-K.W. Roggenkamp: A characterization of orders of finite lattice type. Invent.Math. 17 (1972), 79–84.
Roggenkamp, K.W.-J. Schmidt: Almost split sequences for integral group rings and orders. Com.in Algebra 4 (1976), 893–917.
Roggenkamp, K.W.: Some examples of orders of global dimension two. Math.Zeit. 154 (1977), 225–238. Orders of global dimension two. Math.Zeit. 160 (1978), 63–67.
Auslander, M.: Representation dimension of Artin algebras. Queen Mary College Math.Notes, London (1971).
Roggenkamp, K.W.: Algebras of global dimension two. Archiv Math. 30 (1978), 385–390.
Roggenkamp,K.W.: Indecomposable representations of orders of global dimension two. (1979), to appear J. of Algebra, pp.19
Ringel, C.M.-K.W.Roggenkamp: Socle determined categories of representations of artinian hereditary tensor algebras. (1979), to appear J. of Algebra, pp. 21.
Reiner, I.: Indecomposable representations of cyclic p-groups. Proc. of the Philadelphia Conference in Representation Theory of Algebras, Lecture in Pure and Applied Math. Vol.37, Marcel Dekker (1978), 425–446.
Auslander,M.: Functors and morphisms determined by objects Ch.III, some special orders. Proc. of the Philadelphia Conference in Representation Theory of Algebras, Lecture in Pure and Applied Math. Vol.37, Marcel Dekker (1978).
Green, E.L.: Diagrammatic techniques in the study of indecomposable modules. Proc. of the Conference in Ring Theory II, Oklahoma, Marcel Dekker (1977), 149–169.
Auslander, M.: Existence theorems for almost split sequences. Proc. of the Conference on Ring Theory II, Oklahoma, Marcel Dekker (1977), 1–44.
Wiedemann,A.: Thesis (1980), Stuttgart.
Bessenrodt,Chr.: Thesis (1980), Essen.
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Roggenkamp, K.W. (1980). The lattice type of orders: A diagrammatic approach. I. In: van Oystaeyen, F. (eds) Ring Theory Antwerp 1980. Lecture Notes in Mathematics, vol 825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089126
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