{"created":"2022-01-28T01:58:14.164853+00:00","id":2006998,"links":{},"metadata":{"_buckets":{"deposit":"e0496b0b-970b-48bc-86ea-77725dd5edc6"},"_deposit":{"id":"2006998","owners":[1],"pid":{"revision_id":0,"type":"depid","value":"2006998"},"status":"published"},"_oai":{"id":"oai:u-ryukyu.repo.nii.ac.jp:02006998","sets":["1642837622505:1642837628262:1642837638076","1642838403551:1642838406414"]},"author_link":[],"item_1617186331708":{"attribute_name":"Title","attribute_value_mlt":[{"subitem_title":"HIRATA SEPARABLE EXTENSION OVER THE DESCENDING CHAIN OF SUBRINGS","subitem_title_language":"en"}]},"item_1617186419668":{"attribute_name":"Creator","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Yamashiro, Yasukazu","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"山城, 康一","creatorNameLang":"ja"}]}]},"item_1617186476635":{"attribute_name":"Access Rights","attribute_value_mlt":[{"subitem_access_right":"open access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_abf2"}]},"item_1617186626617":{"attribute_name":"Description","attribute_value_mlt":[{"subitem_description":"In [5], we considered the equivalent class of desending chains of subrings. In this note, we consider Hirata separable extension (H-separable extension) over the desending chain of subrings. Let Λ be a ring, Γ a subring of Λ, C the center of Λ and Δ the commutater of Γ in Λ. Λ is a Hirata separabale extension over Γ if and only if Δ is C-finitely generated projective and Λ ⊗_γ Λ ≅ Hom_c(Δ , Λ) by the map a ⊗ b → [d → adb], where a ⊗ b ∈ Λ ⊗_γ Λ and d ∈ Δ (Theorem 1.1 in [3]).","subitem_description_type":"Other"},{"subitem_description":"紀要論文","subitem_description_type":"Other"}]},"item_1617186643794":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_publisher":"Department of Mathematical Science, Faculty of Science, University of the Ryukyus","subitem_publisher_language":"en"}]},"item_1617186702042":{"attribute_name":"Language","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_1617186783814":{"attribute_name":"Identifier","attribute_value_mlt":[{"subitem_identifier_type":"HDL","subitem_identifier_uri":"http://hdl.handle.net/20.500.12000/23607"}]},"item_1617186920753":{"attribute_name":"Source Identifier","attribute_value_mlt":[{"subitem_source_identifier":"1344-008X","subitem_source_identifier_type":"ISSN"},{"subitem_source_identifier":"AA10779580","subitem_source_identifier_type":"NCID"}]},"item_1617186941041":{"attribute_name":"Source Title","attribute_value_mlt":[{"subitem_source_title":"Ryukyu mathematical journal","subitem_source_title_language":"en"}]},"item_1617187056579":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2011-12","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"121","bibliographicPageStart":"117","bibliographicVolumeNumber":"24"}]},"item_1617258105262":{"attribute_name":"Resource Type","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_1617265215918":{"attribute_name":"Version Type","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_be7fb7dd8ff6fe43","subitem_version_type":"NA"}]},"item_1617605131499":{"attribute_name":"File","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_access","filename":"Vol24p117.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2006998/files/Vol24p117.pdf"},"version_id":"42c8d653-d2e7-4d09-a70d-8b87aac38a14"}]},"item_title":"HIRATA SEPARABLE EXTENSION OVER THE DESCENDING CHAIN OF SUBRINGS","item_type_id":"15","owner":"1","path":["1642837638076","1642838406414"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2012-03-02"},"publish_date":"2012-03-02","publish_status":"0","recid":"2006998","relation_version_is_last":true,"title":["HIRATA SEPARABLE EXTENSION OVER THE DESCENDING CHAIN OF SUBRINGS"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-10-31T03:13:01.926839+00:00"}