{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T07:23:50Z","timestamp":1695799430012},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","funder":[{"name":"National Science Foundation","award":["DMS 1500254"],"award-info":[{"award-number":["DMS 1500254"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:p> We investigate when fiber products of lattices are finitely generated and obtain a new characterization of bounded lattice homomorphisms onto lattices satisfying a property we call Dean\u2019s condition (D) which arises from Dean\u2019s solution to the word problem for finitely presented lattices. In particular, all finitely presented lattices and those satisfying Whitman\u2019s condition satisfy (D). For lattice epimorphisms [Formula: see text], [Formula: see text], where [Formula: see text], [Formula: see text] are finitely generated and [Formula: see text] satisfies (D), we show the following: If [Formula: see text] and [Formula: see text] are bounded, then their fiber product (pullback) [Formula: see text] is finitely generated. While the converse is not true in general, it does hold when [Formula: see text] and [Formula: see text] are free. As a consequence, we obtain an (exponential time) algorithm to decide boundedness for finitely presented lattices and their finitely generated sublattices satisfying (D). This generalizes an unpublished result of Freese and Nation. <\/jats:p>","DOI":"10.1142\/s0218196720500174","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T15:58:02Z","timestamp":1575302282000},"page":"693-710","source":"Crossref","is-referenced-by-count":1,"title":["Bounded homomorphisms and finitely generated fiber products of lattices"],"prefix":"10.1142","volume":"30","author":[{"given":"William","family":"DeMeo","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Colorado, Boulder, Co, USA"}]},{"given":"Peter","family":"Mayr","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Colorado, Boulder, Co, USA"}]},{"given":"Nik","family":"Ru\u0161kuc","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of St Andrews, St Andrews, Scotland, UK"}]}],"member":"219","published-online":{"date-parts":[[2020,1,28]]},"reference":[{"key":"S0218196720500174BIB001","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/pdn039"},{"key":"S0218196720500174BIB003","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/042"},{"key":"S0218196720500174BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-44236-5_2"},{"key":"S0218196720500174BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-7204-0725-9.50025-3"},{"key":"S0218196720500174BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2017.09.035"},{"key":"S0218196720500174BIB007","doi-asserted-by":"publisher","DOI":"10.1112\/jlms.12221"},{"key":"S0218196720500174BIB008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1972-0313141-1"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196720500174","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T07:51:50Z","timestamp":1592553110000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196720500174"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,28]]},"references-count":7,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["10.1142\/S0218196720500174"],"URL":"https:\/\/doi.org\/10.1142\/s0218196720500174","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,28]]}}}