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Algebra Comput."],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:p> We initiate the study of expansions of monoids in the class of two-sided restriction monoids and show that generalizations of the Birget\u2013Rhodes prefix group expansion, despite the absence of involution, have rich structure close to that of relatively free inverse monoids. <\/jats:p><jats:p> For a monoid [Formula: see text] and a class of partial actions of [Formula: see text], determined by a set, [Formula: see text], of identities, we define [Formula: see text] to be the universal [Formula: see text]-generated two-sided restriction monoid with respect to partial actions of [Formula: see text] determined by [Formula: see text]. This is an [Formula: see text]-restriction monoid which (for a certain [Formula: see text]) generalizes the Birget\u2013Rhodes prefix expansion [Formula: see text] of a group [Formula: see text]. Our main result provides a coordinatization of [Formula: see text] via a partial action product of the idempotent semilattice [Formula: see text] of a similarly defined inverse monoid, partially acted upon by [Formula: see text]. The result by Fountain, Gomes and Gould on the structure of the free two-sided restriction monoid is recovered as a special case of our result. <\/jats:p><jats:p> We show that some properties of [Formula: see text] agree well with suitable properties of [Formula: see text], such as being cancellative or embeddable into a group. We observe that if [Formula: see text] is an inverse monoid, then [Formula: see text], the free inverse monoid with respect to strong premorphisms, is isomorphic to the Lawson\u2013Margolis\u2013Steinberg generalized prefix expansion [Formula: see text]. This gives a presentation of [Formula: see text] and leads to a model for [Formula: see text] in terms of the known model for [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196719500590","type":"journal-article","created":{"date-parts":[[2019,7,29]],"date-time":"2019-07-29T22:42:20Z","timestamp":1564440140000},"page":"1467-1498","source":"Crossref","is-referenced-by-count":14,"title":["Two-sided expansions of monoids"],"prefix":"10.1142","volume":"29","author":[{"given":"Ganna","family":"Kudryavtseva","sequence":"first","affiliation":[{"name":"University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova Cesta 2, SI-1000 Ljubljana, Slovenia"},{"name":"Institute of Mathematics, Physics and Mechanics, Jadranska Ulica 19, SI-1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,10,24]]},"reference":[{"key":"S0218196719500590BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-1236(02)00032-0"},{"key":"S0218196719500590BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(84)90092-6"},{"key":"S0218196719500590BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(89)90199-3"},{"key":"S0218196719500590BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-009-8025-1"},{"key":"S0218196719500590BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8130-3"},{"key":"S0218196719500590BIB006","doi-asserted-by":"publisher","DOI":"10.1215\/ijm\/1399395828"},{"key":"S0218196719500590BIB007","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/007.1"},{"key":"S0218196719500590BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2011.10.015"},{"key":"S0218196719500590BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s40863-018-0087-y"},{"key":"S0218196719500590BIB011","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-98-04575-4"},{"key":"S0218196719500590BIB012","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300012973"},{"key":"S0218196719500590BIB013","doi-asserted-by":"publisher","DOI":"10.1080\/00927879908826450"},{"key":"S0218196719500590BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196709005214"},{"key":"S0218196719500590BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-005-0522-0"},{"key":"S0218196719500590BIB016","doi-asserted-by":"publisher","DOI":"10.1080\/00927870008841083"},{"key":"S0218196719500590BIB017","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196796000404"},{"key":"S0218196719500590BIB019","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788708000542"},{"key":"S0218196719500590BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-006-0665-7"},{"issue":"3","key":"S0218196719500590BIB021","first-page":"519","volume":"73","author":"Hollings C.","year":"2007","journal-title":"Acta Sci. 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