The concept of isoclinism on the class of groups was introduced by Philip Hall in 1940. Then, in 1993, Moneyhun used this concept on Lie algebras. In this paper, we study the notion of isoclinism on pairs of Lie rings, and some results are obtained when two isoclinic pairs of Lie rings are given. In particular, we prove that every isoclinism class of pairs of Lie rings contains at least one stem pair.
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