Embedding into 2-generated simple associative (Lie) algebras

References

• Albert, A. A. (1950). A note on the exceptional Jordan algebra. Proc. Nat. Acad. Sci. U.S.A. 36:372–374.
   PubMed Web of Science ®Google Scholar
• Bahturin, Y., Olshanskii, A. (2011). Filtrations and distortion in infinite-dimensional algebras. J. Algebra 327:251–291.
   Web of Science ®Google Scholar
• Bergman, G. M. (1978). The diamond lemma for ring theory. Adv. Math. 29:178–218.
   Web of Science ®Google Scholar
• Bokut, L. A. (1962). Embedding algebras into algebraically closed Lie algebras. Dokl. Akad. Nauk SSSR 14(5):963–964.
   Google Scholar
• Bokut, L. A. (1962). Embedding Lie algebras into algebraically closed Lie algebras. Algebra Logika 1(2):47–53.
   Google Scholar
• Bokut, L. A. (1963). Some embedding theorems for rings and semigroups. I, II. Sibirsk. Mat. Zh. 4:500–518, 729–743.
   Google Scholar
• Bokut, L. A. (1972). Unsolvability of the word problem, and subalgebras of finitely presented Lie algebras. Izv. Akad. Nauk. SSSR Ser. Mat. 36:1173–1219.
   Google Scholar
• Bokut, L. A. (1976). Imbeddings into simple associative algebras. Algebra Logika 15:117–142.
   Google Scholar
• Bokut, L. A. (1978). Imbedding into algebraically closed and simple Lie algebras. Trudy Mat. Inst. Steklov. 148:30–42.
   Google Scholar
• Bokut, L. A., Chen, Y. (2007). Gröbner–Shirshov basis for free Lie algebras: After A.I. Shirshov. Southeast Asian Bull. Math. 31:1057–1076.
   Google Scholar
• Bokut, L. A., Chen, Y., Deng, X. (2010). Gröbner–Shirshov bases for Rota-Baxter algebras. Siberian Math. J. 51(6):978–988.
   Web of Science ®Google Scholar
• Bokut, L. A., Chen, Y., Li, Y. (2008). Gröbner–Shirshov bases for Vinberg-Koszul-Gerstenhaber right-symmetric algebras. Fund. Appl. Math. 14(8):55–67 (in Russian). J. Math. Sci. 2010, 166:603–612.
   Google Scholar
• Bokut, L. A., Chen, Y., Liu, C. (2010). Gröbner–Shirshov bases for dialgebras. Int. J. Algebra Comput. 20(3):391–415.
   Web of Science ®Google Scholar
• Bokut, L. A., Chen, Y., Mo, Q. (2010). Gröbner–Shirshov bases and embeddings of algebras. Int. J. Algebra Comput. 20:875–900.
   Web of Science ®Google Scholar
• Bokut, L. A., Chen, Y., Mo, Q. (2013). Gröbner–Shirshov bases for semirings. J. Algebra 385:47–63.
   Web of Science ®Google Scholar
• Bokut, L. A., Chen, Y., Qiu, J. (2010). Gröbner–Shirshov bases for associative algebras with multiple operations and free Rota-Baxter algebras. J. Pure Appl. Algebra 214:89–100.
   Web of Science ®Google Scholar
• Bokut, L. A., Fong, Y., Ke, W.-F. (2004). Composition-Diamond lemma for associative conformal algebras. J. Algebra 272:739–774.
   Web of Science ®Google Scholar
• Bokut, L. A., Kang, S.-J., Lee, K.-H., Malcolmson, P. (1999). Gröbner–Shirshov bases for Lie super-algebras and their universal enveloping algebras. J. Algebra 217:461–495.
   Web of Science ®Google Scholar
• Bokut, L. A., Kukin, G. P. (1994). Algorithmic and Combinatorial Algebra. Dordrecht: Kluwer Academic Publishers.
   Google Scholar
• Bokut, L. A., Malcolmson, P. (1999). Gröbner–Shirshov bases for relations of a Lie algebra and its enveloping algebra. Algebra Combinator. (Hong Kong) Singapore: Springer, pp. 47–54.
   Google Scholar
• Buchberger, B. (1965). An algorithm for finding a basis for the residue class ring of a zero-dimensional polynomial ideal [in German]. Ph.D. thesis. University of Innsbruck, Austria.
   Google Scholar
• Buchberger, B. (1970). An algorithmical criteria for the solvability of algebraic systems of equations [in German]. Aequ. Math. 4:374–383.
   Google Scholar
• Chen, K. T., Fox, R. H., Lyndon, R. C. (1958). Free differential calculus, IV: The quotient groups of the lower central series. Ann. Math. 68:81–95.
   Web of Science ®Google Scholar
• Chen, Y., Chen, Y., Zhong, C. (2010). Composition-Diamond lemma for modules. Czech. Math. J. 60(135):59–76.
   Web of Science ®Google Scholar
• Chibrikov, E. S. (2004). On free Lie conformal algebras. Vestnik Novosib. State Univ. 4(1):65–83.
   Google Scholar
• Cohn, P. M. (1961). On the embedding of rings in skew fields. Proc. London Math. Soc. 11(3):511–530.
   Google Scholar
• Evans, T. (1952). Embedding theorems for multiplicative systems and projective geometries. Proc. Amer. Math. Soc. 3:614–620.
   Web of Science ®Google Scholar
• Filippov, V. T. (1981). On the chains of varieties generated by free Maltsev and alternative algebras. Dokl. Akad. Nauk SSSR 260(5):1082–1085.
   Google Scholar
• Filippov, V. T. (1984). Varieties of Malcev and alternative algebras generated by algebras of finite rank. Groups and other algebraic systems with finiteness conditions. Trudy Inst. Mat., Nauka Sibirsk. Otdel. Novosibirsk 4:139–156.
   Google Scholar
• Goryushkin, A. P. (1974). Imbedding of countable groups in 2-generated simple groups. Math. Notes 16:725–727.
   Google Scholar
• Hall, P. (1974). On the embedding of a group in a join of given groups. J. Austral. Math. Soc. 17:434–495.
   Google Scholar
• Higman, G. (1951). A finitely generated infinite simple group. J. London Math. Soc. 26:61–64.
   Google Scholar
• Higman, G., Neumann, B. H., Neumann, H. (1949). Embedding theorems for groups. J. London Math. Soc. 24: 247–254.
   Google Scholar
• Hironaka, H. (1964). Resolution of singularities of an algebraic variety over a field if characteristic zero, I, II. Ann. Math. 79:109–203, 205–326.
   Web of Science ®Google Scholar
• Ivanov, I. S. (1965). Free T-sums of multioperator fields. Dokl. Akad. Nauk SSSR 165:28–30; Soviet Math. Dokl. 6: 1398–1401.
   Google Scholar
• Ivanov, I. S. (1967). Free T-sums of multioperator fields. Trudy Mosk. Mat. Obshch. 17:3–44.
   Google Scholar
• Kang, S.-J., Lee, K.-H. (2000). Gröbner-Shirshov bases for irreducible sln+1-modules. J. Algebra 232:1–20.
   Web of Science ®Google Scholar
• Kurosh, A. G. (1969). Multioperators rings and algebras. Russ. Math. Surveys. Uspekhi 24(1):3–15.
   Google Scholar
• Lyndon, R. C. (1954). On Burnside’s problem. Trans. Am. math. Soc. 77:202–215.
   Google Scholar
• Malcev, A. I. (1952). On a representation of nonassociative rings [In Russian]. Uspekhi Mat. Nauk N.S. 7:181–185.
   Google Scholar
• Mikhalev, A. A. (1989). The junction lemma and the equality problem for color Lie superalgebras. Vestnik Moskov. Univ. Ser. I Mat. Mekh. 5:88–91. English translation: Moscow Univ. Math. Bull. 44:87–90.
   Google Scholar
• Mikhalev, A. A. (1992). The composition lemma for color Lie superalgebras and for Lie p-superalgebras. Contemp. Math. 131(2):91–104.
   Google Scholar
• Mikhalev, A. A. (1995). Shirshov’s composition techniques in Lie superalgebra (non-commutative Gröbner bases). Trudy. Sem. Petrovsk. 18:277–289. English translation: J. Math. Sci. 1996, 80:2153–2160.
   Google Scholar
• Novikov, P. S. (1958). On the algorithmic unsolvability of the word problem in group theory. AMS Translations 9:1–122.
   Google Scholar
• Shestakov, I. P. (1978). A problem of Shirshov. Algebra Logic 16:153–166.
   Google Scholar
• Shirshov, A. I. (1956). On special J-rings. Mat. Sb. 38:149–166.
   Google Scholar
• Shirshov, A. I. (1958). On free Lie rings. Mat. Sb. 45:13–21.
   Google Scholar
• Shirshov, A. I. (1962). Some algorithmic problem for Lie algebras. Sibirsk. Mat. Z. 3:292–296 (in Russian); English translation In SIGSAM Bull. 1999, 33(2):3–6.
   Google Scholar
• Shirshov, A. I. (1962). Some algorithmic problem for 𝜀-algebras. Sibirsk. Mat. Z. 3:132–137.
   Google Scholar
• Selected works of Shirshov, A. I., Eds. Bokut, L. A., Latyshev, V., Shestakov, I., Zelmanov, E., Trs. Bremner, M., Kochetov, M. (2009). Birkhäuser, Basel, Boston, Berlin.
   Google Scholar
• Skornyakov, L. A. (1958). Non-associative free T-sums of fields. Mat. Sb. 44:297–312.
   Google Scholar
• Shutov, E. G. (1963). Embeddings of semigroups in simple and complete semigroups. Mat. Sb. 62(4):496–511.
   Google Scholar
• Ufnarovski, V. A. (1995). Combinatorial and asymptotic methods in algebra. Encyclopaedia Mat. Sci. 57:1–196.
   Google Scholar