{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:27:13Z","timestamp":1775464033346,"version":"3.50.1"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","funder":[{"name":"Centre for Mathematics of the University of Coimbra","award":["UID\/MAT\/00324\/2013"],"award-info":[{"award-number":["UID\/MAT\/00324\/2013"]}]},{"name":"Teoria de Lie y Teoria de Espacios de Banach","award":["FQM298"],"award-info":[{"award-number":["FQM298"]}]},{"name":"Teoria de Lie y Teoria de Espacios de Banach","award":["FQM7156"],"award-info":[{"award-number":["FQM7156"]}]},{"name":"Spanish Ministerio de Educacion y Ciencia","award":["MTM2013-41208P"],"award-info":[{"award-number":["MTM2013-41208P"]}]},{"name":"Fundacao para a Ciencia e a Tecnologia","award":["SFRH\/BPD\/101675\/2014"],"award-info":[{"award-number":["SFRH\/BPD\/101675\/2014"]}]},{"name":"Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia","award":["FEDER-UCA18-107643"],"award-info":[{"award-number":["FEDER-UCA18-107643"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Algebra Appl."],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:p> We introduce the class of split Lie\u2013Rinehart algebras as the natural extension of the one of split Lie algebras. We show that if [Formula: see text] is a tight split Lie\u2013Rinehart algebra over an associative and commutative algebra [Formula: see text] then [Formula: see text] and [Formula: see text] decompose as the orthogonal direct sums [Formula: see text] and [Formula: see text], where any [Formula: see text] is a nonzero ideal of [Formula: see text], any [Formula: see text] is a nonzero ideal of [Formula: see text], and both decompositions satisfy that for any [Formula: see text], there exists a unique [Formula: see text] such that [Formula: see text]. Furthermore, any [Formula: see text] is a split Lie\u2013Rinehart algebra over [Formula: see text]. Also, under mild conditions, it is shown that the above decompositions of [Formula: see text] and [Formula: see text] are by means of the family of their, respective, simple ideals. <\/jats:p>","DOI":"10.1142\/s0219498821501644","type":"journal-article","created":{"date-parts":[[2020,5,12]],"date-time":"2020-05-12T03:17:08Z","timestamp":1589253428000},"page":"2150164","source":"Crossref","is-referenced-by-count":5,"title":["Split Lie\u2013Rinehart algebras"],"prefix":"10.1142","volume":"20","author":[{"given":"Helena","family":"Albuquerque","sequence":"first","affiliation":[{"name":"University of Coimbra, CMUC, Department of Mathematics, Apartado 3008, 3001-454 Coimbra, Portugal"}]},{"given":"Elisabete","family":"Barreiro","sequence":"additional","affiliation":[{"name":"University of Coimbra, CMUC, Department of Mathematics, Apartado 3008, 3001-454 Coimbra, Portugal"}]},{"given":"A. 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