
doi: 10.1007/bf01194384
Let \(A\) be a finite dimensional algebra over an algebraically closed field \(k\) and suppose that \(A\) has cubed zero radical. We show that if \(\text{Ext}^i_A(DA,A)=0\) for all \(i\geq 1\) then \(A\) is self-injective, where \(D=\Hom_k(-,k)\), and that if \(A\) is self-injective then every finitely generated \(A\)-module \(M\) with \(\text{Ext}^i_A(M,M)=0\) for \(i\geq 1\) is projective.
Centralizing and normalizing extensions, Injective modules, self-injective associative rings, Free, projective, and flat modules and ideals in associative algebras, radical cube zero algebras, finitely generated modules, finite dimensional algebras, Finite rings and finite-dimensional associative algebras, self-injective algebras, Jacobson radical, quasimultiplication
Centralizing and normalizing extensions, Injective modules, self-injective associative rings, Free, projective, and flat modules and ideals in associative algebras, radical cube zero algebras, finitely generated modules, finite dimensional algebras, Finite rings and finite-dimensional associative algebras, self-injective algebras, Jacobson radical, quasimultiplication
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