Citation: | 羽 李. The ``Freedom Theorem" of Left-Commutative Algebras[J]. Journal of South China Normal University (Natural Science Edition), 2018, 50(1): 110-113. |
[1] L.A. Bokut and G.P. Kukin. Algorithmic and combinatorial algebra., Mathematics and its Applications 255. Kluwer Academic Publishers Group, Dordrecht, 1994.
[2] A. Dzhumadil'daev and C. L\"{o}fwall. Trees, free right-symmetric algebras, free Novikov algebras and identities. Homology, Homotopy and Applications. 4(2)(2002), 165–190. [3] D. Kozybaev, L. Makar-Limanov and U. Umirbaev. The freiheitssatz and automorphisms of free right-symmetric algebras. Asian-European Journal of Mathematics. 1(2)(2008), 243-254. [4] J.-L. Loday. Cup product for Leibniz cohomology and dual Leibniz algebras. Math. Scand. 77, Univ. Louis Pasteur, Strasbourg, 1995, 189-196. [5] W. Magnus. \"{U}ber discontinuierliche Gruppen mit einer definierenden Relation (Der Freiheitssaz). J. Reine Angew. Math. 163(1930), 141-165. [6] L. Makar-Limanov. Algebraically closed skew fields. J. Algebra 93(1985), 117-135. [7] N.S. Romanovskii. A theorem on freeness for groups with one defining relation in varieties of solvable and nilpotent groups of given degrees.(Russian) Mat. Sb. (N.S.) 89(131)(1972), 93-99. [8] A.I. Shirshov. Some algorithmic problems for Lie algebras. Sibirsk. Mat. Z. 3(1962), 292-296.
[1] L.A. Bokut and G.P. Kukin. Algorithmic and combinatorial algebra., Mathematics and its Applications 255. Kluwer Academic Publishers Group, Dordrecht, 1994.
[2] A. Dzhumadil'daev and C. L\"{o}fwall. Trees, free right-symmetric algebras, free Novikov algebras and identities. Homology, Homotopy and Applications. 4(2)(2002), 165–190. [3] D. Kozybaev, L. Makar-Limanov and U. Umirbaev. The freiheitssatz and automorphisms of free right-symmetric algebras. Asian-European Journal of Mathematics. 1(2)(2008), 243-254. [4] J.-L. Loday. Cup product for Leibniz cohomology and dual Leibniz algebras. Math. Scand. 77, Univ. Louis Pasteur, Strasbourg, 1995, 189-196. [5] W. Magnus. \"{U}ber discontinuierliche Gruppen mit einer definierenden Relation (Der Freiheitssaz). J. Reine Angew. Math. 163(1930), 141-165. [6] L. Makar-Limanov. Algebraically closed skew fields. J. Algebra 93(1985), 117-135. [7] N.S. Romanovskii. A theorem on freeness for groups with one defining relation in varieties of solvable and nilpotent groups of given degrees.(Russian) Mat. Sb. (N.S.) 89(131)(1972), 93-99. [8] A.I. Shirshov. Some algorithmic problems for Lie algebras. Sibirsk. Mat. Z. 3(1962), 292-296. |