Prinjective modules, propartite modules, representations of bocses and lattices over orders
ジャーナル
フリー
1997 年 49 巻 1 号 p. 31-68
詳細
- Published: 1997 Received: 1993/06/14 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: Wrong : 1) N. Bourbaki, Algébre Commutative, Paris, Hermann, 1965, 1968, 1969.
2) W. W. Crawley-Boevey, On tame algebras and bocses, Proc. London Math. Soc., 56 (1988), 451-483.
3) E. Dieterich, Reduction of isolated singularities, Comment. Math. Helv., 62 (1987), 654-676.
4) Ju. A. Drozd, Tame and wild matrix problems (in Russian), in Representations and Quadratic Forms, Kiev 1979, pp. 39-74.
5) J. A. Drozd and M. G. Greuel, Tame-wild dichotomy for Cohen-Macaulay modules, Math. Ann., 294 (1992), 387-394.
6) H. Fujita and K. Nishida, Tilting lattices over orders associated with simple modules, Tsukuba J. Math., 15 (1991), 529-546.
7) E. L. Green and I. Reiner, Integral representations and diagrams, Michigan Math. J., 25 (1978), 53-84, (1988), 312-336.
8) S. Kasjan, On Prinjective modules, tameness and the Tits form, Bull. Polish Acad. Sci. Math., 41 (1993), 327-341.
9) S. Kasjan, Adjustment functors and tame representation type, Comm. Algebra, 22 (1994), 5587-5597.
10) S. Kasjan and D. Simson, Varieties of poset representations, tameness and minimal posets of wild prinjective type, in Proceedings of the Sixth International Conference on Representations of Algebras, Canadian Mathematical Society Conference Proceedings, Vol. 14, 1993, pp. 245-284.
11) H. Kraft, Geometric methods in representation theory, in Representations of Algebras, in Lecture Notes in Math., No. 944, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1982, pp. 180-258.
12) H. Lenzing and D. Simson, Cohen-Macaulay modules, representations of posets and tiled orders, in preparation.
13) K. Nishida, Representations of orders and vector space categories, J. Pure Appl. Algebra, 33 (1984), 209-217.
14) J. A. de la Peña, Functors preserving tameness, Fund. Math., 137 (1991), 177-185.
15) J. A. de la Peña, On the dimension of the module varieties of tame and wild algebras, Comm. Algebra, 19 (1991), 1795-1807.
16) J. A, de la Penn and D. Simson, Prinjective modules, reflection functors, quadratic forms and Auslander-Reiten sequences, Trans. Amer. Math. Soc., 329 (1992), 733-753.
17) I. Reiner, Maximal Orders, Academic Press, London-New York-San Francisco, 1975.
18) C. M. Ringel and K. W. Roggenkamp, Diagrammatic methods in the representation theory of orders, J. Algebra, 60 (1979), 11-42.
19) A. V. Roiter, Matrix problems and representations of bocses (in Russian), in Representations and Quadratic Forms, Kiev 1979, 3-38.
20) D. Simson, Vector space categories, right peak rings and their socle projective modules, J. Algebra, 92 (1985), 532-571.
21) D. Simson, A narrow over-ring adjustment functor, J. Algebra, 136 (1991), 463-496.
22) D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra, Logic and Applications, Vol. 4, Gordon & Breach Science Publishers, 1992.
23) D. Simson, Posets of finite prinjective type and a class of orders, J. Pure Appl. Algebra, 90 (1993), 77-103.
24) D. Simson, On representation types of module subcategories and orders, Bull. Polish Acad. Sci. Math., 41 (1993), 77-93.
25) D. Simson, Representation embedding problems, categories of extensions and prinjective modules, Canad. Math. Soc. Conf. Proc., 18 (1996), 601-639.
26) S. O. Smal∅, Functorial finite subcategories over triangular matrix rings, Proc. Amer. Math. Soc., 111 (1991), 651-656.
27) K. Yamagata, On the representation theory of BOCS's, in Proceedings of Representation Theory Conference, Shimoda (Japan), 2.-5. November 1982, pp. 284-296, (in Japanese).
28) K. Yamagata, Frobenius algebras, in Handbook of Algebra, (ed. M. Hazewinkel), Vol. 1, North-Holland Elsevier, 1996, pp. 841-887.
Right : [1] N. Bourbaki, Algébre Commutative, Paris, Hermann, 1965, 1968, 1969.
[2] W. W. Crawley-Boevey, On tame algebras and bocses, Proc. London Math. Soc., 56 (1988), 451-483.
[3] E. Dieterich, Reduction of isolated singularities, Comment. Math. Helv., 62 (1987), 654-676.
[4] Ju. A. Drozd, Tame and wild matrix problems (in Russian), in Representations and Quadratic Forms, Kiev 1979, pp. 39-74.
[5] J. A. Drozd and M. G. Greuel, Tame-wild dichotomy for Cohen-Macaulay modules, Math. Ann., 294 (1992), 387-394.
[6] H. Fujita and K. Nishida, Tilting lattices over orders associated with simple modules, Tsukuba J. Math., 15 (1991), 529-546.
[7] E. L. Green and I. Reiner, Integral representations and diagrams, Michigan Math. J., 25 (1978), 53-84, (1988), 312-336.
[8] S. Kasjan, On Prinjective modules, tameness and the Tits form, Bull. Polish Acad. Sci. Math., 41 (1993), 327-341.
[9] S. Kasjan, Adjustment functors and tame representation type, Comm. Algebra, 22 (1994), 5587-5597.
[10] S. Kasjan and D. Simson, Varieties of poset representations, tameness and minimal posets of wild prinjective type, in Proceedings of the Sixth International Conference on Representations of Algebras, Canadian Mathematical Society Conference Proceedings, Vol. 14, 1993, pp. 245-284.
[11] H. Kraft, Geometric methods in representation theory, in Representations of Algebras, in Lecture Notes in Math., No. 944, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1982, pp. 180-258.
[12] H. Lenzing and D. Simson, Cohen-Macaulay modules, representations of posets and tiled orders, in preparation.
[13] K. Nishida, Representations of orders and vector space categories, J. Pure Appl. Algebra, 33 (1984), 209-217.
[14] J. A. de la Peña, Functors preserving tameness, Fund. Math., 137 (1991), 177-185.
[15] J. A. de la Peña, On the dimension of the module varieties of tame and wild algebras, Comm. Algebra, 19 (1991), 1795-1807.
[16] J. A, de la Peña and D. Simson, Prinjective modules, reflection functors, quadratic forms and Auslander-Reiten sequences, Trans. Amer. Math. Soc., 329 (1992), 733-753.
[17] I. Reiner, Maximal Orders, Academic Press, London-New York-San Francisco, 1975.
[18] C. M. Ringel and K. W. Roggenkamp, Diagrammatic methods in the representation theory of orders, J. Algebra, 60 (1979), 11-42.
[19] A. V. Roiter, Matrix problems and representations of bocses (in Russian), in Representations and Quadratic Forms, Kiev 1979, 3-38.
[20] D. Simson, Vector space categories, right peak rings and their socle projective modules, J. Algebra, 92 (1985), 532-571.
[21] D. Simson, A narrow over-ring adjustment functor, J. Algebra, 136 (1991), 463-496.
[22] D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra, Logic and Applications, Vol. 4, Gordon & Breach Science Publishers, 1992.
[23] D. Simson, Posets of finite prinjective type and a class of orders, J. Pure Appl. Algebra, 90 (1993), 77-103.
[24] D. Simson, On representation types of module subcategories and orders, Bull. Polish Acad. Sci. Math., 41 (1993), 77-93.
[25] D. Simson, Representation embedding problems, categories of extensions and prinjective modules, Canad. Math. Soc. Conf. Proc., 18 (1996), 601-639.
[26] S. O. Smal∅, Functorial finite subcategories over triangular matrix rings, Proc. Amer. Math. Soc., 111 (1991), 651-656.
[27] K. Yamagata, On the representation theory of BOCS's, in Proceedings of Representation Theory Conference, Shimoda (Japan), 2.-5. November 1982, pp. 284-296, (in Japanese).
[28] K. Yamagata, Frobenius algebras, in Handbook of Algebra, (ed. M. Hazewinkel), Vol. 1, North-Holland Elsevier, 1996, pp. 841-887.
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