Details:
Title  Gr\"obnerShirshov bases for $L$algebras.  Author(s)  Leonid A. Bokut, YuFu Chen, Jiapeng Huang  Type  Article in Journal  Abstract  In this paper, we first establish CompositionDiamond lemma for Ωalgebras. We give a Gröbner–Shirshov basis of the free Lalgebra as a quotient algebra of a free Ωalgebra, and then the normal form of the free Lalgebra is obtained. Second we establish CompositionDiamond lemma for Lalgebras. As applications, we give Gröbner–Shirshov bases of the free dialgebra and the free product of two Lalgebras, and then we show four embedding theorems of Lalgebras: (1) Every countably generated Lalgebra can be embedded into a twogenerated Lalgebra. (2) Every Lalgebra can be embedded into a simple Lalgebra. (3) Every countably generated Lalgebra over a countable field can be embedded into a simple twogenerated Lalgebra. (4) Three arbitrary Lalgebras A, B, C over a field k can be embedded into a simple Lalgebra generated by B and C if k ≤ dim(B * C) and A ≤ B * C, where B * C is the free product of B and C.
 Keywords  Gröbner–Shirshov basis; Ωalgebra; dialgebra; Lalgebra  ISSN  02181967; 17936500/e 
URL 
http://www.worldscientific.com/doi/abs/10.1142/S0218196713500094 
Language  English  Journal  Int. J. Algebra Comput.  Volume  23  Number  3  Pages  547571  Publisher  World Scientific, Singapore  Year  2013  Edition  0  Translation 
No  Refereed 
No 
