Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
Categories of lattices, and their global structure in terms of almost split sequences
Репозиторій DSpace/Manakin
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Categories of lattices, and their global structure in terms of almost split sequences
Інший ID:
2000 Mathematics Subject Classification: 16G30, 16G70, 18E10; 16G60.
Посилання:
Categories of lattices, and their global structure in terms of almost split sequences / W. Rump // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 1. — С. 87–111. — Бібліогр.: 30 назв. — англ.
Дата:
2004
Переглядів:
513
Завантажень:
192
Анотація:
A major part of Iyama’s characterization of
Auslander-Reiten quivers of representation-finite orders Λ consists
of an induction via rejective subcategories of Λ-lattices, which
amounts to a resolution of Λ as an isolated singularity. Despite
of its useful applications (proof of Solomon’s second conjecture
and the finiteness of representation dimension of any artinian algebra), rejective induction cannot be generalized to higher dimensional Cohen-Macaulay orders Λ. Our previous characterization
of finite Auslander-Reiten quivers of Λ in terms of additive functions [22] was proved by means of L-functors, but we still had to
rely on rejective induction. In the present article, this dependence
will be eliminated.
