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ON INVARIANCE OF RECURSIVE DIFFERENTIABILITY UNDER TH E ISOTOPY OF LEFT BOL LOOPS
(CEP USM, 2007) Larionova-Cojocaru, Inga; Syrbu, Parascovia
We prove that the recursive derivatives of order 1 of isotopic left Bol loops are isotopic and that every loop, isotopic to a recursively 1-differentiable left Bol loop, is recursively 1-differentiable.The recursive differentiability of di-associative loops is also considered.
ON RECURSIVE DIFFERENTIABILITY OF BINARY QUASIGROUPS
(CEP USM, 2015) Larionova-Cojocaru, Inga; Syrbu, Parascovia
Recursively differentiable binary quasigroups and loops, are considered in the present paper. Invariants under the recursive differentiability of binary quasigroups are found. It is shown that the recursive derivative of order one of an LIP-loop (Q;) (in particular of a left Bol loop) is an isostrophe of its core. The recursively 1-differentiable left Bol loops are studied. Some properties of recursive derivatives of order one of left Bol loops are established.