Abstract:
We prove that each degenerate alternative algebra of characteristic $\ne2$ contains a nonzero ideal with an additive basis consisting of the absolute zero divisors of an arbitrary large order. As a corollary we establish the existence of infinitely many nonisomorphic commutative prime alternative algebras and existence of infinite series of strict and nonstrict exceptional alternative algebras with different sets of proper identities.
Keywords:alternative algebra, absolute zero divisor of an arbitrary order, exceptional prime algebra, C-operation, identity, alternative monster, isotope.