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Algebras stably equivalent to Nakayama algebras of Loewy length at most 4

Published online by Cambridge University Press:  09 April 2009

Idun Reiten
Idun Reiten
Affiliation:
Department of MathematicsUniversity of Trondheim, NLHT 7000 Trondheim, Norway
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Abstract

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Two artin algebras Λ and Λ′ are said to be stably equivalent if their categories of finitely generated modules modulo projectives are equivalent. In this paper a characterization is given of the artin algebras stably equivalent to Nakayama algebras of Loewy length (at most) four. The proof is an illustration of the technique of using irreducible maps to study problems about stable equivlence.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 1 , February 1979 , pp. 37 - 50
Copyright
Copyright © Australian Mathematical Society 1979

References

Auslander, M. and Reiten, I. (1973), ‘Stable equivalence of artin algebras’, Proc. Conf. on orders, group rings and related topics, pp. 8–64 (Lecture Notes in Mathematics 353, Springer Verlag, New York).CrossRefGoogle Scholar
Auslander, M. and Reiten, I. (1975), ‘Stable equivalence of dualizing R-varieties III: Dualizing R-varieties stably equivalent to hereditary dualizing R-varieties’, Adv. in Math. 17, 122–142.CrossRefGoogle Scholar
Auslander, M. and Reiten, I. (1977a), ‘Representation theory of artin algebras IV: Invariants given by almost split sequences’, Comm. in Algebra 5 (5), 443–518.CrossRefGoogle Scholar
Kupisch, H. (1959), ‘Beiträge zur Theorie nichthalbeinfacher Ringe mit Minimalbedingung’, J. Reine Angew. Math. 201, 100–112.CrossRefGoogle Scholar
Murase, I. (1964), ‘On the structure of generalized uniserial rings III’, Sci. Pap. Coll. Gen. Educ. Univ. Tokyo 14, 11–25.Google Scholar
Reiten, I. (1975), ‘Stable equivalence of dualizing R-varieties VI: Nakayama dualizing R-varieties’, Adv. in Math. 17, 196–211.CrossRefGoogle Scholar
Reiten, I. (1976), ‘Stable equivalence of self injective algebras’, J. of Algebra 14 (1), 63–74.CrossRefGoogle Scholar
Reiten, I. (1977), ‘Correction to my paper on Nakayama R-varieties’, Adv. in Math. 23, 211–212.CrossRefGoogle Scholar
Reiten, I. (1978), ‘A note on stable equivalence and Nakayama algebras’, Proc. Amer. Math. Soc. (to appear).CrossRefGoogle Scholar