Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
1. Introduction.............5
2. Basic dimension of artin rings................7
3. Cobasic dimension of artin rings............8
4. Basic dimension of algebras stably equivalent to an hereditary artin algebra............12
5. Hereditary artin algebras of global basic and cobasic dimension 1....................17
6. Global basic and cobasic dimensions of radical squared zero algebras............34
References...............43
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
232
Liczba stron
43
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXXXII
Daty
wydano
1984
Twórcy
autor
- Humboldt-Universität, Sektion Mathematik, DDR - 1086 Berlin, Unter Den Linden 6 (PF 1297)
autor
- Institute of Mathematics, N. Copernicus University, 87-100 Toruń, Chopina 12/18, Polska
Bibliografia
- [1] M. Auslander, Large modules over artin algebras, in: Algebra, Topology and Categories, Academic Press (1976). 1-17.
- [2] M. Auslander, Representation theory of artin algebras II. Comm. Algebra 1 (1974). 269-310.
- [3] M. Auslander and I. Reiten, Representation theory of artin algebras III, Comm. Algebra 3 (1975), 239-294.
- [4] M. Auslander and I. Reiten, Stable equivalence of artin algebras, Proc. Conf. on orders, group rings and related topics, Springer Lecture Notes 353, 1973, 8-71.
- [5] M. Auslander, E. L. Green and I. Reiten, Modules with waists, Illinois J. Math. 19 (1975), 467-478.
- [6] S. Brenner and M. C. R. Butler, Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors, Proceedings ICRA-II, Springer Lecture Notes 832, 1980, 103-169.
- [7] V. Dlab and C. M. Ringel, On algebras of finite representation type, J. Algebra 33 (1975), 306-394.
- [8] V. Dlab and C. M. Ringel, Representations of graphs and algebras. Memoirs Amer. Math. Soc. 173 (1976).
- [9] D. Eisenbud and P. Griffith, The structure of serial rings, Pacific J. Math. 36 (1972), 109-121.
- [10] P. Gabriel, Unzerlegbare Darstellungen I. Manuscripta Mathematica 6 (1972), 71 103.
- [11] P. Gabriel, Indecomposable representations II, Symp. Math. Inst. Naz. Alta. Mat. 11 (1973), 81-104.
- [12] R. Gordon and E. L. Green, Modules with cores and amalgamations of indecomposable modules. Memoirs Amer. Math. Soc. 187 (1977).
- [13] E. L. Green, On the structure of indecomposable modules, Proc. Conf. on Representation Theory (Philadelphia 1976), Lect. Notes in Pure and Appl. Math, 37, Marcel Dekker, 1978, 369-380.
- [14] D. Happel and C. M. Ringel, Tilted algebras, Trans. Amer. Math. Soc., 274 (1982), 399-443.
- [15] H. Meitzer and A. Skowroński, A hierarchy of rings of finite representation type. Bull. Acad. Polon. Sci., Ser. Sci. Math. 30 (1982), 21-23.
- [16] T. Nakayama, On Frobeniusean algebras II, Ann. of Math. 42 (1940), 1-22.
- [17] M. I. Platzeck, On algebras stably equivalent to an hereditary artin algebra, Canad. J. Math. 30 (1978), 817-829.
- [18] M. I. Platzeck, Representation theory of algebras stably equivalent to an hereditary artin algebra, Trans. Amer. Math. Soc. 238 (1978). 89-128.
- [19] D. Simson and A. Skowroński, Extensions of artinian rings by hereditary injective modules, Proceedings ICRA-III, Puebla 1980, Lecture Notes in Math. 903, 1981, 315-330.
- [20] A. Skowroński, On the structure of indencomposable modules over artin algebras, Coll. Math., to appear.
- [21] A. Skowroński, A characterization of a new class of artin algebras, J. London Math. Soc., 26 (1982), 53-63.
- [22] A. Tachikawa, On algebras of which every indecomposable representation has an irreducible one as the top or the bottom Loewy constituent. Math. Z. 75 (1961), 215-227.
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