×

zbMATH — the first resource for mathematics

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

MSC:
16Gxx Representation theory of associative rings and algebras
16P10 Finite rings and finite-dimensional associative algebras
03C60 Model-theoretic algebra
PDF BibTeX XML Cite
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.