Nucleus and center of certain non power associative algebras - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T18:27:53Z http://mathoverflow.net/feeds/question/81878 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/81878/nucleus-and-center-of-certain-non-power-associative-algebras Nucleus and center of certain non power associative algebras Phys student 2011-11-25T12:43:42Z 2011-11-25T17:26:50Z <p>I am looking for an example of a noncommutative and non power associative n - dimensional algebra \$A\$ with \$N(A)=Z(A)\$, where \$N(A)\$ is the nucleus and \$Z(A)\$ the center. All the examples coming to my mind are algebras with \$Z(A)\subseteq N(A)\$</p> <p>Thank you</p> http://mathoverflow.net/questions/81878/nucleus-and-center-of-certain-non-power-associative-algebras/81889#81889 Answer by James for Nucleus and center of certain non power associative algebras James 2011-11-25T14:32:44Z 2011-11-25T17:26:50Z <p>I think the following example works. Take an algebra \$A\$ (say, over \$\mathbb{Z}\$) with basis \$\{ a, b, c \}\$ and with products defined by putting \$cb = c^2 = b\$, and all other products of basis elements equal to \$a\$. Then \$(cc)c = bc = a\$, while \$c(cc) = cb = c\$, so \$A\$ is not power-associative and non-commutative. But the centre and nucleus are equal (to \$\mathbb{Z}a\$).</p>