{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T15:40:22Z","timestamp":1727970022633},"reference-count":37,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:p>A subdirect product [Formula: see text] is global if there is a topology on [Formula: see text] which makes of [Formula: see text] the algebra of all global sections of a sheaf whose stalks are the algebras [Formula: see text] with [Formula: see text]. A quasivariety [Formula: see text] has BL-global representations if there is a class [Formula: see text] containing but close to the class of all relatively subdirectly irreducible members of [Formula: see text], satisfying that every member of [Formula: see text] is isomorphic to a global subdirect product whose factors are in [Formula: see text]. The adjective \u201cBL\u201d refers to \u201cBirkhoff-like\u201d since this type of representations are analogous to the classical Birkhoff subdirect representation by relatively subdirectly irreducibles. This paper has two main contributions. The first one is a generalization of a theorem proved in [D. Vaggione, Sheaf representation and Chinese remainder theorems, Algebra Universalis\u00a029 (1992) 232\u2013272] which characterizes the existence of a global representation of an algebra in terms of the solvability of certain congruence systems. The second one is a theorem assuring the existence of BL-global representations for quasivarieties with a near unanimity term.<\/jats:p>","DOI":"10.1142\/s0218196722500692","type":"journal-article","created":{"date-parts":[[2022,9,9]],"date-time":"2022-09-09T15:52:33Z","timestamp":1662738753000},"page":"1545-1566","source":"Crossref","is-referenced-by-count":0,"title":["BL-global representations"],"prefix":"10.1142","volume":"32","author":[{"given":"D.","family":"Vaggione","sequence":"first","affiliation":[{"name":"FAMAF, Facultad de Matem\u00e1tica, Astronom\u00eda, F\u00edsica y Computaci\u00f3n, Universidad Nacional de C\u00f3rdoba, C\u00f3rdoba, Argentina"}]}],"member":"219","published-online":{"date-parts":[[2022,11,8]]},"reference":[{"key":"S0218196722500692BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01187059"},{"volume-title":"Distributive Lattices","year":"1974","author":"Balbes R.","key":"S0218196722500692BIB002"},{"key":"S0218196722500692BIB003","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1006\/aima.2000.1962","volume":"159","author":"Blanco J.","year":"2001","journal-title":"Adv. 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