A note on the number of subquantales

作者:Han, Shengwei*; Zhao, Bin; Wang, Shunqin
来源:ALGEBRA UNIVERSALIS, 2013, 69(2): 191-200.
DOI:10.1007/s00012-013-0221-8

摘要

In this note, it is proved for n <= 5 that if Q is a finite quantale with vertical bar Q vertical bar >= n, then there are at least n subquantales of Q. However, the result does not hold when vertical bar Q vertical bar >= 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.

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