On some small cardinals for Boolean algebras

Assume that all. algebras are atomless. (1) Spind(A x B) = Spind(A) U Spind(B). (2)Spind(Pi(iis an element ofl)(W) A(i)) = {omega} boolean OR U-iis an element ofl Spind(A(i)). Now suppose that kappa and lambda are infinite cardinals, with kappa uncountable and regular and with kappa < lambda. (3) There is an atomless Boolean algebra A such that u(A) = kappa and i(A) = lambda. (4) If lambda is also regular, then there is an atontless Boolean algebra A such that t(A) = s(A) = kappa and a(A) = lambda. All results are in ZFC. and answer some problems posed in Monk [01] and Monk [infinity].