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 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 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>