Details:
Title  Gr\"obnerShirshov bases and embeddings of algebras.  Author(s)  Leonid A. Bokut, YuFu Chen, Qiuhui Mo  Type  Article in Journal  Abstract  In this paper, by using Gröbner–Shirshov bases, we show that in the following classes, each (respectively, countably generated) algebra can be embedded into a simple (respectively, twogenerated) algebra: associative differential algebras, associative Ωalgebras, associative λdifferential algebras. We show that in the following classes, each countably generated algebra over a countable field k can be embedded into a simple twogenerated algebra: associative algebras, semigroups, Lie algebras, associative differential algebras, associative Ωalgebras, associative λdifferential algebras. We give another proofs of the well known theorems: each countably generated group (respectively, associative algebra, semigroup, Lie algebra) can be embedded into a twogenerated group (respectively, associative algebra, semigroup, Lie algebra).
 Keywords  Gröbner–Shirshov basis; group; associative algebra; Lie algebra; associative differential algebra; associative Ωalgebra  ISSN  02181967; 17936500/e 
URL 
http://www.worldscientific.com/doi/abs/10.1142/S0218196710005923 
Language  English  Journal  Int. J. Algebra Comput.  Volume  20  Number  7  Pages  875900  Publisher  World Scientific, Singapore  Year  2010  Edition  0  Translation 
No  Refereed 
No 
