{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T13:32:52Z","timestamp":1649079172576},"reference-count":7,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008,1,1]]},"abstract":"<jats:title>General Theory of Quasi-Commutative BCI-algebras<\/jats:title><jats:p>It is known that commutative BCK-algebras form a variety, but BCK-algebras do not [4]. Therefore H. Yutani introduced the notion of quasicommutative BCK-algebras. In this article we first present the notion and general theory of quasi-commutative BCI-algebras. Then we discuss the reduction of the type of quasi-commutative BCK-algebras and some special classes of quasicommutative BCI-algebras.<\/jats:p>","DOI":"10.2478\/v10037-008-0030-2","type":"journal-article","created":{"date-parts":[[2009,3,21]],"date-time":"2009-03-21T01:07:26Z","timestamp":1237597646000},"page":"253-258","source":"Crossref","is-referenced-by-count":0,"title":["General Theory of Quasi-Commutative BCI-algebras"],"prefix":"10.2478","volume":"16","author":[{"given":"Tao","family":"Sun","sequence":"first","affiliation":[]},{"given":"Weibo","family":"Pan","sequence":"additional","affiliation":[]},{"given":"Chenglong","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Xiquan","family":"Liang","sequence":"additional","affiliation":[]}],"member":"374","reference":[{"key":"1","first-page":"91","article-title":"The ordinal numbers","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"key":"2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2478\/v10037-007-0001-z","article-title":"Several classes of BCI-algebras and their properties","volume":"1","author":"Yuzhong Ding","year":"2007","journal-title":"Formalized Mathematics"},{"key":"3","first-page":"175","article-title":"Congruences and quotient algebras of BCI-algebras","volume":"4","author":"Yuzhong Ding","year":"2007","journal-title":"Formalized Mathematics"},{"key":"4","author":"Jie Meng","year":"2001","journal-title":"An Introduction to BCI-algebras"},{"key":"5","doi-asserted-by":"crossref","first-page":"237","DOI":"10.2478\/v10037-007-0027-2","article-title":"Several classes of BCK-algebras and their properties","volume":"4","author":"Tao Sun","year":"2007","journal-title":"Formalized Mathematics"},{"key":"6","first-page":"187","article-title":"Boolean domains","volume":"1","author":"Andrzej Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"7","first-page":"67","article-title":"Properties of subsets","volume":"1","author":"Zinaida Trybulec","year":"1990","journal-title":"Formalized Mathematics"}],"container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/16\/3\/article-p253.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2008.16.issue-3\/v10037-008-0030-2\/v10037-008-0030-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,30]],"date-time":"2020-05-30T15:27:28Z","timestamp":1590852448000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10037-008-0030-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,1]]},"references-count":7,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/v10037-008-0030-2","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2008,1,1]]}}}