{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T09:25:51Z","timestamp":1768728351462,"version":"3.49.0"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2025,3]]},"abstract":"<jats:p> A submonoid of the additive group [Formula: see text] is called a Puiseux monoid if it consists of non-negative rationals. Given a monoid M, the set consisting of all non-empty finite subsets of M is also a monoid under the Minkowski sum, and it is called the (finitary) power monoid of M. In this paper, we study atomicity and factorization properties in the setting of power monoids of Puiseux monoids. We specifically focus on the ascent of atomicity and the finite factorization property (although we also consider the ascending chain condition on principal ideals and the length-finite factorization property). We prove that the finite factorization property ascends from any Puiseux monoid to its power monoid. On the other hand, we construct an atomic Puiseux monoid whose power monoid is not atomic. We also prove that the existence of maximal common divisors for non-empty finite subsets is a sufficient condition for the property of being atomic to ascend from a Puiseux monoid to its power monoid. <\/jats:p>","DOI":"10.1142\/s0218196724500565","type":"journal-article","created":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T11:02:46Z","timestamp":1730286166000},"page":"167-181","source":"Crossref","is-referenced-by-count":1,"title":["On the atomicity of power monoids of Puiseux monoids"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-8740-7600","authenticated-orcid":false,"given":"Victor","family":"Gonzalez","sequence":"first","affiliation":[{"name":"Department of Mathematics, Miami Dade College, Miami, FL 33135, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1465-0227","authenticated-orcid":false,"given":"Eddy","family":"Li","sequence":"additional","affiliation":[{"name":"The Nueva School, San Mateo, CA 94403, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-8807-2123","authenticated-orcid":false,"given":"Henrick","family":"Rabinovitz","sequence":"additional","affiliation":[{"name":"Melrose School, Melrose, MA 02176, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-8106-9185","authenticated-orcid":false,"given":"Pedro","family":"Rodriguez","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Clemson University, Clemson, SC 29634, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-6666-2762","authenticated-orcid":false,"given":"Marcos","family":"Tirador","sequence":"additional","affiliation":[{"name":"Matcom, Universidad de La Habana, Habana 10400, Cuba"}]}],"member":"219","published-online":{"date-parts":[[2025,1,14]]},"reference":[{"key":"S0218196724500565BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(90)90074-R"},{"key":"S0218196724500565BIB002","series-title":"Springer Proceedings in Mathematics & Statistics","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/978-981-16-8422-7_2","volume-title":"Rings, Monoids, and Module Theory","volume":"382","author":"Anderson D. 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