Gröbner–Shirshov bases for commutative dialgebras

References

• Adams, W. W., Loustaunau, P. (1994). An Introduction to Gröbner Bases. Graduate Studies in Mathematics, Vol. 3. Providence, RI: American Mathematical Society.
   Google Scholar
• Bergman, G. M. (1978). The diamond lemma for ring theory. Adv. Math. 29(2):178–218.
   Web of Science ®Google Scholar
• Bokut, L. A. (1976). Imbeddings into simple associative algebras. Algebra i 15(2):73–142.
   Google Scholar
• Bokut, L. A., Chen, Y. (2008). Gröbner-Shirshov bases: some new results. In: Proceedings of the Second International Congress in Algebra and Combinatorics. World Scientific, pp. 35–56.
   Google Scholar
• Bokut, L. A., Chen, Y. (2014). Gröbner-Shirshov Bases and Shirshov Algorithm, Educational Tutorial Lecture Notes. Novosibirsk: Novosibirsk State University.
   Google Scholar
• Bokut, L. A., Chen, Y., Liu, C. (2010). Gröbner-Shirshov bases for dialgebras. Int. J. Algebra Comput. 20(03):391–415.
   Google Scholar
• Bokut, L. A., Fong, Y., Ke, V.-F., Kolesnikov, P. S. (2000). Gröbner and gröbner-Shirshov bases in algebra, and conformal algebras. Fund. Prikl. Mat. 6(3):669–706.
   Google Scholar
• Bokut, L. A., Kolesnikov, P. S. (2000). Gröbner-Shirshov bases: from inception to the present time, Zap. Nauchn. Sem. St.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 272(Vopr. Teor. Predst. Algebr i Grupp. 7) 26–67, 345.
   Google Scholar
• Bokut, L. A., Kolesnikov, P. S. (2004). Gröbner-Shirshov bases, conformal algebras, and pseudo-algebras. Sovrem. Mat. Prilozh. 131:92–130.
   Google Scholar
• Bokut, L. A., Kukin, G. P. (1994). Algorithmic and Combinatorial Algebra, Mathematics and its Applications, Vol. 255. Dordrecht: Kluwer Academic Publishers Group.
   Google Scholar
• Bokut, L. A., Shum, K. P. (2005). Gröbner and Gröbner-Shirshov bases in algebra: an elementary approach. Southeast Asian Bull. Math. 29(2):227–252.
   Google Scholar
• Buchberger, B. (1965). Ein algorithmus zum auffinden der basiselemente des restklassenringes nach einem nulldimensionalen polynomideal, Ph.D. thesis, University of Innsbruck.
   Google Scholar
• Buchberger, B. (1970). Ein algorithmisches kriterium für die lösbarkeit eines algebraischen gleichungssystems. Aeq. Math. 4(3):374–383.
   Google Scholar
• Buchberger, B., Collins, G., Loos, R., Albrecht, R. (1982). Computer Algebra, Symbolic and Algebraic Computation, Computing Supplementum, Vol. 4. New York: Springer.
   Google Scholar
• Buchberger, B., Winkler, F. (1998). Gröbner Bases and Applications, London Mathematical Society Lecture Note Series, Vol. 251. Cambridge: Cambridge University Press.
   Google Scholar
• Cox, D. A., Little, J., O’Shea, D. (2015). Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, Undergraduate Texts in Mathematics, 4th ed. Cham: Springer.
   Google Scholar
• Eisenbud, D. (1995). Commutative Algebra: With a View toward Algebraic Geometry, Graduate Texts in Mathematics, Vol. 150. New York: Springer.
   Google Scholar
• Eisenbud, D., Peeva, I., Sturmfels, B. (1998). Non-commutative Gröbner bases for commutative algebras. Proc. Am. Math. Soc. 126(03):687–691.
   Google Scholar
• Hironaka, H. (1964). Resolution of singulatities of an algebtaic variety over a field if charac-teristic zero, I, II. Math. Ann. 79(2):205–208.
   Google Scholar
• Kolesnikov, P. S. (2008). Varieties of dialgebras, and conformal algebras. Sib. Math. J. 49(2):257–339.
   Web of Science ®Google Scholar
• Loday, J.-L. (1993). Une version non commutative des algèbres de lie: les algèbres de leibniz. Enseign. Math. 39(3-4):269–293.
   Google Scholar
• Loday, J.-L. (1995). Algèbres ayant deux opérations associatives (digèbres), C. R. Acad. Sci. Paris Sér. I Math. 321(2):141–146.
   Google Scholar
• Loday, J.-L., Frabetti, A., Chapoton, F., Goichot, F. (2001). Dialgebras and Related Operads. Lecture Notes in Mathematics, Vol. 1763. Berlin: Springer.
   Google Scholar
• Newman, M. H. A. (1942). On theories with a combinatorial definition of “equivalence. Ann. Math. 43(2):223–243.
   Google Scholar
• Pozhidaev, A. P. (2009). 0-dialgebras with bar-unity and nonassociative Rota-Baxter algebras. Sib. Math. J. 50(6):1070–1369.
   Web of Science ®Google Scholar
• Shirshov, A. I. (1962). Some algorithmic problems for ε-algebras. Sibirsk. Mat. Ž. 3:132–137.
   Google Scholar
• Shirshov, A. I. (2009). Selected works of A. I. Shirshov (Translated from the Russian by Murray Bremner and Mikhail V. Kotchetov, Edited by Leonid A. Bokut, Victor Latyshev, Ivan Shestakov and Efim Zelmanov) Contemporary Mathematicians. Basel: Birkhäuser.
   Google Scholar
• Zhang, G., Chen, Y. (2017). A new composition-Diamond lemma for dialgebras. Algebra Colloq. 24(2):323–350.
   Web of Science ®Google Scholar
• Zhuchok, A. V. (2010). Free commutative dimonoids. Algebra Discrete Math. 9(1):109–119.
   Web of Science ®Google Scholar