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As congruences on rings are characterized by their ideals, this notion is a straightforward generalization of the notion from ring theory: a ring is simple in the sense that it has no nontrivial ideals if and only if it is simple in the sense of universal algebra. The same remark applies with respect
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Magari, R. (1969). "Una dimostrazione del fatto che ogni varietĂ ammette algebre semplici".
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to groups and normal subgroups; hence the universal notion is also a generalization of a
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Lampe, W.A.; Taylor, W. (1982). "Simple algebras in varieties".
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in 1969 asserts that every variety contains a simple algebra.
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127:Annalli dell'UniversitĂ di Ferrara, Sez. VII
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123:The original paper is
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105:(1): 36–43.
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