English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

A triangular matrix ring A is defined by a triplet (R,S,M) where R and S arerings and M is an S-R-bimodule. In the main theorem of this paper we show thatif T is a tilting S-module, then under certain homological conditions on M asan S-module, one can extend T to a tilting complex over A inducing a derivedequivalence between A and another triangular matrix ring specified by(S',R,M'), where the ring S' and the R-S'-bimodule M' depend only on T and M,and S' is derived equivalent to S. Note that no conditions on the ring R areneeded.  These conditions are satisfied when S is an Artin algebra of finite globaldimension and M is finitely generated as an S-module. In this case,$(S',R,M')=(S,R,DM)$ where D is the duality on the category of finitelygenerated S-modules. They are also satisfied when S is arbitrary, M has afinite projective resolution as an S-module, and $\Ext^n_S(M,S)=0$ for all$n>0$. In this case, $(S',R,M')=(S,R,\Hom_S(M,S))$.Comment: 16 pages; major revision, formulated the result in greater generalit

Derived Equivalences of Triangular Matrix Rings Arising from Extensions of Tilting Modules