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Let $m$ be a natural number with prime factorisation $m=p_1^{a_1}\dots p_r^{a_r}$. I'm interested in a special name for the lattice of divisors of $m$, when all exponents are equal: $a_1=a_2=\dots=a_r$. I once saw such a name in a textbook on logic and/or lattice theory but can not find it anymore.

ChatGPT also doesnt know it and using google was also not successful. So I thought about asking here.

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    $\begingroup$ This is just a product of finite chains. I do not know any special name when the chains in the product all have the same size. (Except of course if all the $a_i=2$ and then we have the Boolean lattice...) $\endgroup$ Commented Feb 21 at 1:04
  • $\begingroup$ @SamHopkins I know. I once saw a name, but I cant find it anymore. Im sure there is one somewhere in the literature. $\endgroup$ Commented Feb 21 at 1:05

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