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Herrmann, Christian; Jensen, Christian U.; Lenzing, Helmut

Applications of model theory to representations of finite-dimensional algebras. (English) Zbl 0445.16020

Math. Z. 178, 83-98 (1981).
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scan of Zbl 0445.16020

Cited in 2 Reviews
Cited in 8 Documents

MSC:

16Gxx Representation theory of associative rings and algebras
16P10 Finite rings and finite-dimensional associative algebras
03C60 Model-theoretic algebra
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Full Text: DOI EuDML

References:

[1] Auslander, M.: Representation theory of Artin algebras II. Comm. Algebra1, 269-310 (1974) · Zbl 0285.16029 · doi:10.1080/00927877409412807
[2] Auslander, M., Reiten, I.: Representation theory of Artin algebras. III. Comm. Algebra3, 239-294 (1975), IV. Comm. Algebra5, 443-518 (1977) · Zbl 0331.16027 · doi:10.1080/00927877508822046
[3] Auslander, M., Platzeck, M.I.: Representation theory of hereditary Artin algebras. In: Representation theory of algebras (R. Gordon, ed.). Proceedings of a Conference (Philadelphiy 1976), pp. 389-424. New York: Marcel Dekker 1978 · Zbl 0378.16014
[4] Bell, J.L., Slomson, A.B.: Models and ultraproducts. Amsterdam: North-Holland 1974 · Zbl 0179.31402
[5] Brown, S.S.: Bounds on transfer principles for algebraically closed and complete discretely valued fields. Mem. Amer. Math. Soc.204 (1978) · Zbl 0383.03022
[6] Chang, C.C., Keisler, H.J.: Model theory. Amsterdam: North-Holland 1977 · Zbl 0423.03041
[7] Eklof, P.C.: Ultraproducts for algebraists. In: Handbook of Mathematical Logic (J. Barwise ed.). Amsterdam: North-Holland 1977
[8] Gabriel, P.: Finite representation type is open. In: Representations of Algebras (V. Dlab and P. Gabriel eds.). Proceedings of the International Conference (Ottawa 1974), pp. 132-155. Lecture Notes in Mathematics488, Berlin-Heidelberg-New York: Springer 1975
[9] Gabriel, P.: Représentations indécomposables. Séminaire Bourbaki: 1973/74, no. 444. Lecture Notes in Mathematics431. Berlin-Heidelberg-New York: Springer 1975
[10] Gabriel, P.: Algébres auto-injectives de représentation fini (d’aprés Christine Riedtmann). Séminaire Bourbaki 1979/80, no.545. (to appear)
[11] Jensen, C.U., Lenzing, H.: Model theory and representations of algebras. In: Representation theory II (V. Dlab and P. Gabriel eds.). Proceedings of the second international conference on Representations of Algebras (Ottawa 1979), pp. 302-310. Lecture Notes in Mathematics832. Berlin-Heidelberg-New York: Springer 1980
[12] Jensen, C.U., Lenzing, H.: Homological dimension and representation type of algebras under base field extension. Preprint · Zbl 0498.16023
[13] Kreisel, G., Krivine, J.L.: Elements of mathematical logic (Model theory). Amsterdam: North-Holland 1971 · Zbl 0219.02037
[14] Nazarova, L.A., Rojter, A.V.: Categorical matrix problems and the conjecture of Brauer-Thrall, Kiev 1973. German transl.: Mitt. Math. Sem. Gießen115, 1-153 (1975)
[15] Riedtmann, C.: Algebren, Darstellungsköcher, Überlagerungen und zurück. Comment. Math. Helv.55, 199-224 (1980) · Zbl 0444.16018 · doi:10.1007/BF02566682
[16] Riedtmann, C.: Representation-finite selfinjective algebras of classA n . In: Representation theory II (V. Dlab and P. Gabriel eds.). Proceedings of the second international Conference on Representations of Algebras (Ottawa 1979), pp. 449-520. Lecture Notes in Mathematics832. Berlin-Heidelberg-New York: Springer 1980
[17] Ringel, C.M.: Report on the Brauer-Thrall conjectures; Rojter’s theorem and the theorem of Nazarova and Rojter. In: Representation Theory I. Proceedings of the workshop on the precent trends in the presentation theory (Ottawa 1979), pp. 104-136. Lecture Notes in Mathematics831. Berlin-Heidelberg-New York: Springer 1980
[18] Rojter, A.V.: The unboundedness of the dimension of the indecomposable representations of algebras that have an infinite number of indecomposable representations. Izv. Acad. Nauk SSSR Ser. Mat.32, 1275-1282 (1968) [Russian]. Engl. Transl.: Math. USSR-Tzo.2, 1223-1230 (1968)
[19] Rose, B.I.: On the Model theory of finite-dimensional algebras. Proc. London Math. Soc. (3)40, 21-39 (1980) · Zbl 0463.03020 · doi:10.1112/plms/s3-40.1.21
[20] Shelah, S.: Classification theory and the number of non-isomorphic models. Amsterdam: North-Holland 1978 · Zbl 0388.03009
[21] Smalø, S.O.: The inductive step of the second Brauer-Thrall conjecture. Canad. J. Math. (to appear) · Zbl 0405.16010
[22] Van den Driess, L.: Model theory of fields. Decidability, and bounds for polynomials ideals. Dissertation, Utrecht 1978
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