{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,3]],"date-time":"2023-09-03T09:30:54Z","timestamp":1693733454267},"reference-count":32,"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":[[2023,3]]},"abstract":"<jats:p> A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. Under certain mild conditions on a positive algebraic number [Formula: see text], the additive monoid [Formula: see text] of the evaluation semiring [Formula: see text] is atomic. The atomic structure of both the additive and the multiplicative monoids of [Formula: see text] has been the subject of several recent papers. Here we focus on the monoids [Formula: see text], and we study its omega-primality and elasticity, aiming to better understand some fundamental questions about their atomic decompositions. We prove that when [Formula: see text] is less than [Formula: see text], the atoms of [Formula: see text] are as far from being prime as they can possibly be. Then we establish some results about the elasticity of [Formula: see text], including that when [Formula: see text] is rational, the elasticity of [Formula: see text] is full (this was previously conjectured by Chapman, Gotti and Gotti). <\/jats:p>","DOI":"10.1142\/s021819672350011x","type":"journal-article","created":{"date-parts":[[2022,11,27]],"date-time":"2022-11-27T17:10:00Z","timestamp":1669569000000},"page":"197-210","source":"Crossref","is-referenced-by-count":1,"title":["On the primality and elasticity of algebraic valuations of cyclic free semirings"],"prefix":"10.1142","volume":"33","author":[{"given":"Nancy","family":"Jiang","sequence":"first","affiliation":[{"name":"Stanford University, Stanford, CA 94305, USA"}]},{"given":"Bangzheng","family":"Li","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, MA 02139, USA"}]},{"given":"Sophie","family":"Zhu","sequence":"additional","affiliation":[{"name":"Williamsville East High School, East Amherst, NY 14051, USA"}]}],"member":"219","published-online":{"date-parts":[[2023,1,14]]},"reference":[{"key":"S021819672350011XBIB002","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1080\/00927872.2020.1820514","volume":"49","author":"Albizu-Campos S.","year":"2021","journal-title":"Comm. 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