Cambridge University PressActa Medica Okayama0027-76302262017Canonical and n-canonical modules of a Noetherian algebra165203ENMitsuyasuHashimotoDepartment of Mathematics, Okayama University We define canonical and -canonical modules of a module-finite algebra over a Noether commutative ring and study their basic properties. Using -canonical modules, we generalize a theorem on -syzygy by Araya and Iima which generalize a well-known theorem on syzygies by Evans and Griffith. Among others, we prove a noncommutative version of Aoyamaâ€™s theorem which states that a canonical module descends with respect to a flat local homomorphism.No potential conflict of interest relevant to this article was reported.Cambridge University PressActa Medica Okayama1047-9511142004Experience over five years using a shunt placed between the right ventricle and the pulmonary arteries during initial reconstruction of hypoplasia of the left heart9095ENShunjiSanoKozoIshinoMasaakiKawadaKoYoshizumiMamoruTakeuchiShin-ichiOhtsukiNo potential conflict of interest relevant to this article was reported.