# Tagged Questions

**2**

votes

**0**answers

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### Pseudovarieties of monoids

All (pseudo)varieties considered here are (pseudo)varieties of monoids.
It is known that any (finite or infinite) monoid that satisfies the identities
\begin{equation}
xhxyty = xhyxty, \quad ...

**5**

votes

**3**answers

170 views

### Locally finite varieties which are not finitely generated

Let $\Sigma$ be a signature consisting of operations with finite arity. Let $\mathcal{V}$ be a variety of algebras for this signature. Further suppose that $\mathcal{V}$ is locally finite i.e. every ...

**3**

votes

**2**answers

295 views

### Are algebraic structures uniquely identifed by their free objects?

It might be a naive question, as I am not a specialist in this field.
This is a follow-up to this question.
I want to study varieties of objects generalizing ordered monoids, in particular using an ...

**7**

votes

**2**answers

296 views

### Is there a general result that theorems about finite structures proved in ZFC can be proved in ZF?

The title question is too vague so let me be specific.
Much of modern finite semigroup theory uses profinite semigroups and properties of profinite semigroups that depend on the existence of prime ...

**7**

votes

**1**answer

598 views

### Lattice-ordered commutative monoids

By a lattice-ordered monoid, I mean a structure $(A,0,{+},{\vee},{\wedge})$ such that $(A,0,{+})$ is a (not necessarily commutative) monoid, $(A,{\vee},{\wedge})$ is a lattice, and the two ...