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TitleGr\"obner-Shirshov bases and embeddings of algebras.
Author(s) Leonid A. Bokut, Yu-Fu Chen, Qiuhui Mo
TypeArticle in Journal
AbstractIn 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, two-generated) algebra: associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We show that in the following classes, each countably generated algebra over a countable field k can be embedded into a simple two-generated algebra: associative algebras, semigroups, Lie algebras, associative differential algebras, associative Ω-algebras, associative λ-differential 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 two-generated group (respectively, associative algebra, semigroup, Lie algebra).

KeywordsGröbner–Shirshov basis; group; associative algebra; Lie algebra; associative differential algebra; associative Ω-algebra
ISSN0218-1967; 1793-6500/e
URL http://www.worldscientific.com/doi/abs/10.1142/S0218196710005923
LanguageEnglish
JournalInt. J. Algebra Comput.
Volume20
Number7
Pages875--900
PublisherWorld Scientific, Singapore
Year2010
Edition0
Translation No
Refereed No
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