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...(S)] ∈ HQ2 (X,Z[Y ]) does not depend on the choice of a region coloring in the same line. Remark 4.7. Similar claims of Lemma 4.5 are proved by Etingof and Graña [8], and Niebrzydowski and Przytycki =-=[19]-=-. 5. Quandle consisting of all parabolic elements of PSL(2,C) In this section, we define a quandle P consisting of all parabolic elements of PSL(2,C). We see that P is identified with (C2 \ {0})/±. 5....

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...ributive structures, with (a) usual shelf (or one-term distributive; cf. ([11]) homology theories; [68], [67]), rack ([27]) and quandle (b) the partial derivatives of M.Niebrzydowski and J.Przytycki (=-=[63]-=-); (c) and the twisted rack homology of J.S.Carter, M.Elhamdadi and M.Saito ([9]). ⊞ The technical sign manipulation (especially heavy for the Chevalley-Eilenberg complex) is controlled either by usin...

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...approximation for torsion. The result in [L-N] is generalized in [N-P-1] and in particular, it is proven there that the torsion part of the homology of the dihedral quandle R3 is annihilated by 3. In =-=[N-P-2]-=- it is conjectured that for a finite quasigroup quandle, torsion of its homology is annihilated by the order of the quandle. The conjecture is proved by T. Nosaka for finite Alexander quasigroup quand...