{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T22:14:59Z","timestamp":1648678499673},"reference-count":21,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,1,1]]},"abstract":"<jats:title>Valuation Theory. Part I<\/jats:title>\n        <jats:p>In the article we introduce a valuation function over a field [1]. Ring of non negative elements and its ideal of positive elements have been also defined.<\/jats:p>","DOI":"10.2478\/v10037-012-0002-4","type":"journal-article","created":{"date-parts":[[2012,9,13]],"date-time":"2012-09-13T01:22:44Z","timestamp":1347499364000},"page":"7-14","source":"Crossref","is-referenced-by-count":0,"title":["Valuation Theory. Part I"],"prefix":"10.2478","volume":"20","author":[{"given":"Grzegorz","family":"Bancerek","sequence":"first","affiliation":[]},{"given":"Hidetsune","family":"Kobayashi","sequence":"additional","affiliation":[]},{"given":"Artur","family":"Korni\u0142owicz","sequence":"additional","affiliation":[]}],"member":"374","reference":[{"key":"1","volume-title":"Algebraic Numbers and Algebraic Functions","author":"Emil Artin","year":"1994"},{"issue":"3","key":"2","first-page":"565","article-title":"Ring ideals","volume":"9","author":"Jonathan Backer","year":"2001","journal-title":"Formalized Mathematics"},{"issue":"1","key":"3","first-page":"41","article-title":"The fundamental properties of natural numbers","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"4","first-page":"91","article-title":"The ordinal numbers","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"5","first-page":"107","article-title":"Segments of natural numbers and finite sequences","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"5","key":"6","first-page":"807","article-title":"Properties of fields","volume":"1","author":"J\u00f3zef Bia\u0142as","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"7","first-page":"175","article-title":"Binary operations","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"8","first-page":"55","article-title":"Functions and their basic properties","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"9","first-page":"153","article-title":"Functions from a set to a set","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"2","key":"10","first-page":"357","article-title":"Partial functions","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"11","first-page":"47","article-title":"Some basic properties of sets","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"4","key":"12","first-page":"573","article-title":"Quotient rings","volume":"13","author":"Artur Korni\u0142owicz","year":"2005","journal-title":"Formalized Mathematics"},{"issue":"2","key":"13","first-page":"335","article-title":"Abelian groups, fields and vector spaces","volume":"1","author":"Eugeniusz Kusak","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"14","first-page":"3","article-title":"Construction of rings and left-, right-, and bi-modules over a ring","volume":"2","author":"Micha\u0142 Muzalewski","year":"1991","journal-title":"Formalized Mathematics"},{"issue":"1","key":"15","first-page":"115","article-title":"Domains and their Cartesian products","volume":"1","author":"Andrzej Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"3","key":"16","first-page":"501","article-title":"Integers","volume":"1","author":"Micha\u0142 Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"5","key":"17","first-page":"821","article-title":"Groups","volume":"1","author":"Wojciech Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"2","key":"18","first-page":"291","article-title":"Vectors in real linear space","volume":"1","author":"Wojciech Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"19","first-page":"67","article-title":"Properties of subsets","volume":"1","author":"Zinaida Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"20","first-page":"73","article-title":"Relations and their basic properties","volume":"1","author":"Edmund Woronowicz","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"21","first-page":"181","article-title":"Relations defined on sets","volume":"1","author":"Edmund Woronowicz","year":"1990","journal-title":"Formalized Mathematics"}],"container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/20\/1\/article-p7.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2012.20.issue-1\/v10037-012-0002-4\/v10037-012-0002-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,30]],"date-time":"2020-05-30T15:28:28Z","timestamp":1590852508000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10037-012-0002-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,1]]},"references-count":21,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/v10037-012-0002-4","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2012,1,1]]}}}