  We prove that the skew Calabi-Yau property is preserved under normal
extension for locally finite positively graded algebras. We also obtain a
homological identity which describes the relationship between the Nakayama
automorphisms of skew Calabi-Yau locally finite positively graded algebras and
their normal extensions. As a preliminary, we show that the Nakayama
automorphisms of skew Calabi-Yau algebras always send a regular normal element
to a multiple of itself by a unit.
