{"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_1551255647225":"HIRATA SEPARABLE EXTENSION OVER THE DESCENDING CHAIN OF SUBRINGS","subitem_1551255648112":"en"}]},"item_1617186419668":{"attribute_name":"Creator","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Yamashiro, Yasukazu","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"\u5c71\u57ce, \u5eb7\u4e00","creatorNameLang":"ja"}]}]},"item_1617186476635":{"attribute_name":"Access Rights","attribute_value_mlt":[{"subitem_1522299639480":"open access","subitem_1600958577026":"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 \u039b be a ring, \u0393 a subring of \u039b, C the center of \u039b and \u0394 the commutater of \u0393 in \u039b. \u039b is a Hirata separabale extension over \u0393 if and only if \u0394 is C-finitely generated projective and \u039b \u2297_\u03b3 \u039b \u2245 Hom_c(\u0394 , \u039b) by the map a \u2297 b \u2192 [d \u2192 adb], where a \u2297 b \u2208 \u039b \u2297_\u03b3 \u039b and d \u2208 \u0394 (Theorem 1.1 in [3]).","subitem_description_type":"Other"},{"subitem_description":"\u7d00\u8981\u8ad6\u6587","subitem_description_type":"Other"}]},"item_1617186643794":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_1522300295150":"en","subitem_1522300316516":"Department of Mathematical Science, Faculty of Science, University of the Ryukyus"}]},"item_1617186702042":{"attribute_name":"Language","attribute_value_mlt":[{"subitem_1551255818386":"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_1522646500366":"ISSN","subitem_1522646572813":"1344-008X"},{"subitem_1522646500366":"NCID","subitem_1522646572813":"AA10779580"}]},"item_1617186941041":{"attribute_name":"Source Title","attribute_value_mlt":[{"subitem_1522650068558":"en","subitem_1522650091861":"Ryukyu mathematical journal"}]},"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_1522305645492":"NA","subitem_1600292170262":"http://purl.org/coar/version/c_be7fb7dd8ff6fe43"}]},"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"}