Derived Equivalences for Triangular Matrix Rings
نویسندگان
چکیده
منابع مشابه
Derived Equivalences for Triangular Matrix Rings
We generalize derived equivalences for triangular matrix rings induced by a certain type of classical tilting module introduced by Auslander, Platzeck and Reiten to generalize reflection functors in the representation theory of quivers due to Bernstein, Gelfand and Ponomarev.
متن کاملDerived Equivalences of Triangular Matrix Rings Arising from Extensions of Tilting Modules
A triangular matrix ring Λ is defined by a triplet (R, S, M) where R and S are rings and RMS is an S-R-bimodule. In the main theorem of this paper we show that if TS is a tilting S-module, then under certain homological conditions on the S-module MS , one can extend TS to a tilting complex over Λ inducing a derived equivalence between Λ and another triangular matrix ring specified by (S′, R, M ...
متن کاملStrongly clean triangular matrix rings with endomorphisms
A ring $R$ is strongly clean provided that every element in $R$ is the sum of an idempotent and a unit that commutate. Let $T_n(R,sigma)$ be the skew triangular matrix ring over a local ring $R$ where $sigma$ is an endomorphism of $R$. We show that $T_2(R,sigma)$ is strongly clean if and only if for any $ain 1+J(R), bin J(R)$, $l_a-r_{sigma(b)}: Rto R$ is surjective. Furt...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2008
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-008-9098-1