Lattice isomorphisms of alternative algebras (Q583352)

This paper deals with the relation between finite dimensional alternative algebras A, B over a field which have isomorphic lattices of subalgebras, extending Barnes work on associative algebras [\textit{D. W. Barnes}, J. Aust. Math. Soc. 6, 106-121 (1966; Zbl 0141.031)]. One of the results says that B is semisimple if A is. Much of the work is (naturally, in view of Barnes paper) dedicated to the case that A is an eight- dimensional Cayley-Dickson algebra; special bases of such algebras are used in the proofs.