Abstract:
We prove that each $c$-isotope of a prime nonassociative $(-1,1)$-algebra is a $(-1,1)$-algebra if and only if the element $c$ lies in the commutative center. Every central $c$-isotope of a $(-1,1)$-monster is demonstrated to be isomorphic to the monster.
Keywords:isotope, central isotope, prime algebra, $(-1,1)$-algebra.