{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T13:30:21Z","timestamp":1773235821809,"version":"3.50.1"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,8]]},"abstract":"<jats:p> Let D be an integral domain. In this paper, we investigate two (integer- or \u221e-valued) invariants \u03c9(D, x) and \u03c9(D) which measure how far a nonzero x \u2208 D is from being prime and how far an atomic integral domain D is from being a unique factorization domain (UFD), respectively. In particular, we are interested in when there is a nonzero (irreducible) x \u2208 D with \u03c9(D, x) = \u221e and the relationship between \u03c9(A, x) and \u03c9(B, x), and \u03c9(A) and \u03c9(B), for an extension A \u2286 B of integral domains and a nonzero x \u2208 A. <\/jats:p>","DOI":"10.1142\/s0218196712500403","type":"journal-article","created":{"date-parts":[[2012,4,18]],"date-time":"2012-04-18T02:32:16Z","timestamp":1334716336000},"page":"1250040","source":"Crossref","is-referenced-by-count":8,"title":["ON BOUNDING MEASURES OF PRIMENESS IN INTEGRAL DOMAINS"],"prefix":"10.1142","volume":"22","author":[{"given":"DAVID F.","family":"ANDERSON","sequence":"first","affiliation":[{"name":"University of Tennessee, Department of Mathematics, Knoxville, TN 37996-1320, USA"}]},{"given":"SCOTT T.","family":"CHAPMAN","sequence":"additional","affiliation":[{"name":"Sam Houston University, Department of Mathematics and Statistics, Box 2206, Huntsville, TX 77341-2206, USA"}]}],"member":"219","published-online":{"date-parts":[[2012,7,11]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(92)90144-5"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(90)90074-R"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(92)90089-5"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1080\/00927878008822469"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1080\/00927871003738998"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498810004221"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-010-9259-5"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(97)00147-3"},{"key":"rf9","first-page":"33","volume":"20","author":"Bastida E.","journal-title":"Michigan Math. J."},{"key":"rf10","first-page":"33","volume":"23","author":"Brewer J.","journal-title":"Michigan Math. J."},{"key":"rf11","unstructured":"S. T.\u00a0Chapman, Zero-Dimensional Commutative Rings, Lecture Notes in Pure and Applied Mathematics\u00a0171 (Dekker, New York, 1995)\u00a0pp. 167\u2013190."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100042791"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-88405-4"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1201\/9781420003208"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2007.10.020"},{"key":"rf16","volume-title":"Multiplicative Ideal Theory","author":"Gilmer R.","year":"1972"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100048532"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3180-4_16"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(90)90074-2"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1976-14130-4"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196712500403","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T15:18:43Z","timestamp":1565104723000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196712500403"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7,11]]},"references-count":20,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2012,7,11]]},"published-print":{"date-parts":[[2012,8]]}},"alternative-id":["10.1142\/S0218196712500403"],"URL":"https:\/\/doi.org\/10.1142\/s0218196712500403","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,7,11]]}}}