Let $A=\mathcal{A}(E,\sigma),A'=\mathcal{A}(E',\sigma')$ be Noetherian Artin-Schelter regular geometric algebras with $\operatorname{dim}_{k}A_{1}=\operatorname{dim}_{k}A_{1}'=n$ , and let $\nu,\nu'$ be generalized Nakayama automorphisms of $A,A'$ . In this paper, we study relationships between the conditions
¶
(A) $A$ is graded Morita equivalent to $A'$ , and
¶
(B) $\mathcal{A}(E,\nu^{*}\sigma^{n})$ is isomorphic to $\mathcal{A}(E',(\nu')^{*}(\sigma')^{n})$ as graded algebras.
¶
It is proved that if $A,A'$ are “generic” 3-dimensional quadratic Artin-Schelter regular algebras, then (A) is equivalent to (B), and if $A,A'$ are $n$ -dimensional skew polynomial algebras, then (A) implies (B).