0

I read here: https://mathoverflow.net/questions/193924/how-to-recognize-if-a-lattice-is-distributive?newreg=1439abdc43e24ebcb32afa0532b74ecb that N5 and M3 lattices are not distributive. So I concluded that these lattices are not Boolean Lattices (Correct me If I am wrong!)

My question is: Is D646 a boolean algebra? I think it is not, because its Hasse diagram is exactly like M3.

Furthermore, this question was in my examination paper: "Is D646 a Boolean Algebra?" I concluded it is not based on the fact that M3 lattices are not distributive.

Thanks!

Community
  • 1
AmN
  • 113

1 Answers1

4

I wasn't familiar with the notation D646, so I googled it and found that it's a French frigate and therefore not a Boolean algebra. A little more googling suggests that it's supposed to be the lattice of divisors of 646. Since 646 is the product of 2, 17, and 19, three distinct primes, its lattice of divisors is an 8-element Boolean algebra. Your reference to M3 suggests that you looked only at the prime divisors, and the trivial divisors 1 and 646, ignoring the other three divisors, 34, 38, and 323.

Andreas Blass
  • 71,833