Let A be an Artin algebra.We investigate subalgebras of A with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
Let A be a finite-dimensional hereditary algebra over an algebraically closed field and A(m) be the m-replicated algebra of A.We prove that the representation dimension of A(m) is at most 3,and that the dominant dimension of A(m) is at least m.
