A note on the number of subquantales.

In this note, it is proved for n ≤ 5 that if Q is a finite quantale with | Q| ≥ n, then there are at least n subquantales of Q. However, the result does not hold when | Q| ≥ 6. Also, an example is given of a sequence of quantales of cardinality p + 2 for p prime, each of which have exactly 5 subquantales. [ABSTRACT FROM AUTHOR]