In this paper we consider a
special case of the following two closely related problems of B. Jónsson:
I. For which infinite cardinals m is there an algebra of power m which has
finitely many operations and satisfies the descending chain condition for
subalgebras.
II. For which infinite cardinals m is there an algebra of power m
which has finitely many operations and has no proper subalgebra of power
m.
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