# Questions tagged [universal-algebra]

The study of algebraic structures and properties applying to large classes of such structures. For example, ideas from group theory and ring theory are extended and considered for structures with other signatures (systems of basic or fundamental operations).

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### How do finite door spaces work?

Recall that a door space is a topological space where every set is either open or closed (or both). A topological space is finite if it has finitely many points. I'm interested in learning about ...
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### Axiomatizability of image of functor

Let $\sigma$ and $\tau$ be first-order languages and let $S$ resp. $T$ be theories (sets of sentences) for $\sigma$ resp. for $\tau$ ($S$ and $T$ possibly empty). Let $\mathcal C$ resp. $\mathcal D$ ...
278 views

### Algebras with finite essential arity

We are talking about algebras in the universal algebraic sense, that is, a set that $A$ is equipped with a set $F$ of finitary operations on $A$. Definition: An algebra $(A,F)$ is said to have ...
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### Do almost-point-transitive algebras generate almost-point-transitive varieties?

Say that an algebra $\mathfrak{A}$ (in the sense of universal algebra) is point-transitive iff for every $a,b\in\mathfrak{A}$ there is a $\pi\in Aut(\mathfrak{A})$ with $\pi(a)=b$. While genuinely ...
939 views

### Ternary associative multiplication

In this answer Brian M. Scott describes the following generalization of a binary associative multiplication to a ternary one: it is a function $$[\cdot,\cdot,\cdot] : G\times G \times G \to G$$ such ...
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### Does the likelihood of these tables exist?

Probably it does, and may be a number near $e^{-3/2}$ for 2-deficient tables. First some background. Early on in my studies of universal algebra, I encountered a result of Vadim Murskii, with the ...
281 views

### What is going on in the field of algebraic logic these days?

I'm doing my masters in Mathematics and took a class in universal algebra and there I learned that for example: Boolean algebras have direct connection with classical logic, Heyting algebras with ...
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### First isomorphism theorem for inverse semigroups together with v-prehomomorphisms?

In this old paper D. B. McAlister has introduced another class of morphisms for inverse semigroups, called v-prehomomorphisms. For such a morphism $\theta : S \to T,$ instead of preserving the ...
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### Function and algebraic system

Let $f$ be a surjective function from $X$ to $\{1,2,3\}$. Let $* :X^2 \to X$, such that $$f(x)\neq f(y) \implies f(x) \neq f(xy)\neq f(y),$$ and $$f(x)=f(y)\implies f(x)=f(xy).$$ Let's call the ...
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### Lawvere theory of Lawvere theories

There is a coloured operad $sOp$ such that $sOp$-algebras are single-coloured operads. This operad has a simple description in terms of generators and relations, say, as an operad $F(X)/R$. There is a ...
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### Birkhoff's theorem with language expansion?

Let $\mathcal V$ be a variety (in the sense of universal algebra). Recall that Birkhoff's theorem characterizes when a class $\mathcal W \subseteq \mathcal V$ of $\mathcal V$-algebras forms a ...