{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T09:25:36Z","timestamp":1648891536365},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p> We continue the study of nil-Armendariz rings, initiated by Antoine, and Armendariz rings. We first examine a kind of ring coproduct constructed by Antoine for which the Armendariz, nil-Armendariz, and weak Armendariz properties are equivalent. Such a ring has an important role in the study of Armendariz ring property and near-related ring properties. We next prove an Antoine's result in relation with the ring coproduct by means of a simpler direct method. In the proof we can observe the concrete shapes of coefficients of zero-dividing polynomials. We next observe the structure of nil-Armendariz rings via the upper nilradicals. It is also shown that a ring R is Armendariz if and only if R is nil-Armendariz if and only if R is weak Armendariz, when R is a von Neumann regular ring. <\/jats:p>","DOI":"10.1142\/s0218196712500592","type":"journal-article","created":{"date-parts":[[2012,8,12]],"date-time":"2012-08-12T20:37:01Z","timestamp":1344803821000},"page":"1250059","source":"Crossref","is-referenced-by-count":6,"title":["NIL-ARMENDARIZ RINGS AND UPPER NILRADICALS"],"prefix":"10.1142","volume":"22","author":[{"given":"DA WOON","family":"JUNG","sequence":"first","affiliation":[{"name":"Department of Mathematics, Pusan National University, Pusan 609-735, Korea"}]},{"given":"NAM KYUN","family":"KIM","sequence":"additional","affiliation":[{"name":"Faculty of Liberal Arts and Sciences, Hanbat National University, Daejeon 305-719, Korea"}]},{"given":"YANG","family":"LEE","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Pusan National University, Pusan 609-735, Korea"}]},{"given":"SUNG PIL","family":"YANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Pusan National University, Pusan 609-735, Korea"}]}],"member":"219","published-online":{"date-parts":[[2012,8,31]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1956-0075933-2"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1080\/00927879808826274"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2008.01.019"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700029190"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1974-0357503-7"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1974-0357502-5"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-10-10252-4"},{"key":"rf8","volume-title":"Von Neumann Regular Rings","author":"Goodearl K. R.","year":"1979"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-120013179"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1080\/00927870600549782"},{"key":"rf11","doi-asserted-by":"crossref","first-page":"57","DOI":"10.4064\/fm-85-1-57-71","volume":"85","author":"Krempa J.","journal-title":"Fund. Math."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0406-7"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1080\/00927870600651398"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-100002173"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.3792\/pjaa.73.14"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2000.8451"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196712500592","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T10:29:41Z","timestamp":1565173781000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196712500592"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,31]]},"references-count":16,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2012,8,31]]},"published-print":{"date-parts":[[2012,9]]}},"alternative-id":["10.1142\/S0218196712500592"],"URL":"https:\/\/doi.org\/10.1142\/s0218196712500592","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,31]]}}}