Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $X$ denote an entropic algebra (see here), which just means that all the operations of $X$ are homomorphisms $X^n \rightarrow X.$ Abelian groups are the classic example. Then for any operation of $X$, we have that if $X_0,\ldots,X_{n-1}$ are substructures of $X$, then so too is $f(X_0,\ldots,X_{n-1});$ because after all homomorphisms preserve substructures.

Question. Is there a name for the algebraic structure induced by the operations of $X$ on the set of all substructures of $X$? A link or reference to some more information would be really nice.

share|cite|improve this question
+1 Good question. I don't know a name for such things. Side question: when you say "substructures of X" do you simply mean "subalgebras of X," or do you mean something more general, maybe encompassing relational structures as well? – William DeMeo Feb 4 '14 at 1:49

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.