On the multiplication algebra of a bernstein algebra^*

^*AMS Subject Classification: 17D92.

Abstract

This paper deals with the way in which some restrictions on the structure of Bernstein algebras and on the multiplication algebra of a Bernstein algebra interrelate, the first class of restrictions being expressed as the vanishing of some products between Peirce subspaces, and the second by bounds on the dimension of the multiplication algebra (or some of its key subspaces). The course of this enquiry leads to the introduction in Section 4 of some new numerical invariants of Bernstein algebras, namely, the dimensions of the subspaces .

^*AMS Subject Classification: 17D92.

^†Sponsored by CNPq Research Fellowship Proc. 300645/93-7.

^‡Sponsored by FAPESP Proc. 95/2251-0.

^§Sponsored by FAPESP Proc. 95/0158-3 and FONDECYT 1980548.

^*AMS Subject Classification: 17D92.

^†Sponsored by CNPq Research Fellowship Proc. 300645/93-7.

^‡Sponsored by FAPESP Proc. 95/2251-0.

^§Sponsored by FAPESP Proc. 95/0158-3 and FONDECYT 1980548.

Notes

^*AMS Subject Classification: 17D92.

^†Sponsored by CNPq Research Fellowship Proc. 300645/93-7.

^‡Sponsored by FAPESP Proc. 95/2251-0.

^§Sponsored by FAPESP Proc. 95/0158-3 and FONDECYT 1980548.