# Tagged Questions

**1**

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### Non-finitely based varieties and pseudovarieties

The variety of semigroups defined by $B=\{xyzt=xzyt, yx^ny=xyx^{n-2}yx:n=2,3,\ldots\}$ is non-finitely based (Perkins). Is the pseudovariety defined by $B$ also non-finitely based?
More generally, if ...

**-1**

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**1**answer

83 views

### Variety of commutative semi group [closed]

V is a variety of commutative semi group satisfying the identity $x^2 = x^3$.
I need to prove that:
$|F_V(\{x_1\dots,x_n\})|$ = $3^n -1$.
Any hints on this ?
$F_V$ is V-free algebra.

**2**

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**3**answers

125 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 ...

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**0**answers

47 views

### Semigroups admitting generating sets which induce a “weight” on elements of the semigroup

Neither universal algebra nor semigroup theory is something I really know much about, so this question might not be appropriate for MO; if so, I'll move it to MSE.
Recently, I've been playing ...

**7**

votes

**2**answers

293 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 ...

**8**

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**3**answers

572 views

### What is the smallest variety of algebras containing all fields?

A field is a ring whose nonzero elements form a commutative group under multiplication. A field is also a commutative inverse semigroup with respect to multiplication. The unique multiplicative ...