Groebner-Shirshov bases for extensions of algebras

Details Groebner-Shirshov bases for extensions of algebras Groebner-Shirshov bases for extensions of algebras

2008-04-04

arxiv.org/abs/0804.0639v1

Algebra Colloq., 16(2)(2009), 283-292.

Mathematics

Rings and Algebras

Scientific paper

An algebra $\cal{R}$ is called an extension of the algebra $M$ by $B$ if
$M^2=0$, $M$ is an ideal of $\cal{R}$ and $\cal{R}$$/M\cong B$ as algebras. In
this paper, by using the Gr\"{o}bner-Shirshov bases, we characterize completely
the extensions of $M$ by $B$. An algorithm to find the conditions of an algebra
$A$ to be an extension of $M$ by $B$ is obtained.

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