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The technique is based on two observations: (1), if<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msup><mml:mrow><mml:mi>\ud835\udd42<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>has the structure of certain normed, associative, commutative, and with a unit, algebras<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>\ud835\udd38<\/mml:mi><\/mml:mrow><\/mml:math>over<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>\ud835\udd42<\/mml:mi><\/mml:mrow><\/mml:math>, then there is a scheme for reducing the system of differential equations to an autonomous ordinary differential equation on one variable of the algebra; (2) a technique, previously introduced for solving differential equations over<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>\u2102<\/mml:mi><\/mml:mrow><\/mml:math>, is shown to work on the class mentioned in the previous paragraph. In particular it is shown that the algebras in question include algebras linearly equivalent to the tensor product of matrix algebras with certain normal forms.<\/jats:p>","DOI":"10.1155\/2012\/753916","type":"journal-article","created":{"date-parts":[[2012,10,1]],"date-time":"2012-10-01T21:06:35Z","timestamp":1349125595000},"page":"1-21","source":"Crossref","is-referenced-by-count":6,"title":["On Solving Systems of Autonomous Ordinary Differential Equations by Reduction to a Variable of an Algebra"],"prefix":"10.1155","volume":"2012","author":[{"given":"Alvaro","family":"Alvarez-Parrilla","sequence":"first","affiliation":[{"name":"Facultad de Ciencias, Universidad Aut\u00f3noma de Baja California, Km. 103 Carretera Tijuana-Ensenada, 22860 Ensenada, BC, Mexico"},{"name":"Grupo Alximia SA de CV, Departamento de Investigaci\u00f3n, Ryerson 1268, Zona Centro, 22800 Ensenada, BC, Mexico"}]},{"given":"Mart\u00edn 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