同调满同态,泛性局部化在代数A和A_kB之间的关系

The relationship of homological ring epimorphisms and universal localizations between algebra Aand AB

设A,B,C是域k上的有限维代数,Γ是一个有限生成A模之间的态射集.本文证明了λkIdB:AkB→CkB是一个同调满同态当且仅当λ:A→C是一个同调满同态.还证明了如果存在CkB是AkB在ΓkB上的一个泛性局部化,则C在A上Γ-可逆的.

Let A,B,Cbe finite dimensional algebras over a field k,and letΓbe a set of morphisms between finite generated proj ective A-modules.This article proves that algebra homomorphismλis a homological ring epimorphism if and only ifλ?kIdB is a homological ring epimorphism,and proves that if there exists a universal localizationλ?IdB:A?B→C?B overΓ?B,thenλ:A→B isΓ-inverting.