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Primary Orders of Finite Representation Type

✍ Scribed by Hiroaki Hijikata; Kenji Nishida

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
513 KB
Volume
192
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Recall the well-known theorem of Drozd and Kirichenko cf. Yu. A. Drozd and Ε½ . . V. V. Kirichenko, Math. USSR IzΒ¨estia 7 1973 , 711᎐732 giving a necessary and sufficient condition for a primary order ⌳ to be of finite representation type. Such Ε½ . ⌳s that satisfy the ''necessary condition'' of the DK-theorem will be studied: 1 Classification of ⌳s will be given, up to the best degree admitting general Ε½ . Ε½ . approach. 2 Auslander᎐Reiten quiver α‘› ⌳ will be determined. In particular, it is finite, giving an alternative proof of the sufficiency part of the DK-theorem.

πŸ“œ SIMILAR VOLUMES

The Best Nondeterministic Representation
The Best Nondeterministic Representations of Finite Orderings
✍ C.R. Vela; A. Bahamonde πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 556 KB

This paper formally presents an algorithm to compute the nondeterministic realization with the least number of states that represents an order relation. For this purpose, each input order relation is considered as a finite automaton in a straightforward way. Then the automaton is subject to an itera