Auslander-Reiten Triangles, Ziegler Spectra and Gorenstein Rings
نویسندگان
چکیده
منابع مشابه
The Auslander-reiten Translate on Monomial Rings
For t in N, E.Miller has defined a category of positively t-determined modules over the polynomial ring S in n variables. We consider the AuslanderReiten translate, Nt, on the (derived) category of such modules. A monomial ideal I is t-determined if each generator x has a ≤ t. We compute the multigraded cohomology and betti spaces of N k t (S/I) for every iterate k and also the S-module structu...
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In this paper, Auslander-Reiten triangles are introduced into algebraic topology, and it is proved that their existence characterizes Poincaré duality spaces. Invariants in the form of quivers are also introduced, and Auslander-Reiten triangles and quivers over spheres are computed. The quiver over the d-dimensional sphere turns out to consist of d − 1 components, each isomorphic to ZA∞. So qui...
متن کاملThe Auslander-reiten Translate on Monomial Quotient Rings
For t in Nn, E.Miller has defined a category of t-determined modules over the polynomial ring S in n variables. We consider the Auslander-Reiten translate, Nt, on the (derived) category of such modules. A monomial ideal I is t-determined if every generator x has a ≤ t. We compute the multigraded cohomologyand betti spaces of N k t (S/I) for every iterate k, and also the Smodule structure of the...
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ژورنال
عنوان ژورنال: K-Theory
سال: 2004
ISSN: 1573-0514,0920-3036
DOI: 10.1023/b:kthe.0000035051.14067.eb