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Results tagged with universal-algebra
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user 57297
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).
8
votes
0
answers
199
views
Varieties of groups with certain properties
Is there an example of a periodic variety $\mathbf{V}$ of groups that satisfies all of the following properties?
$\mathbf{V}$ is finitely based
$\mathbf{V}$ contains finitely many subvarieties
$\mat …
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5
votes
Locally finite varieties which are not finitely generated
Many small semigroups generate varieties that contain non-finitely generated subvarieties. For instance, the 3-element semigroup $\langle a,1\,|\,a^2=0\rangle$ and the 4-element semigroup $\langle a,b …
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5
votes
0
answers
137
views
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 xhytxy=x …
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3
votes
0
answers
140
views
Non-finitely based varieties and pseudovarieties
The variety of semigroups defined by $B=\Big\{(x^py^p)^2=(y^px^p)^2:p \text{ is prime}\Big\}$ is non-finitely based (Isbell, 1970). Is the pseudovariety defined by $B$ also non-finitely based?
More g …
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3
votes
Example of a non-finitely based variety with explicit set of defining identities
There are a few examples that are finitely generated.
(1) Let $L$ be Lyndon's groupoid given by the following multiplication table:
\begin{array} [c]{c|ccccccc}
L & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hl …
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3
votes
1
answer
206
views
Join prime pseudovarieties
A pseudovariety $\mathbf{V}$ of groups is join prime if for any pseudovarieties $\mathbf{V}_1, \mathbf{V}_2, \ldots,\mathbf{V}_m$, the implication $$\mathbf{V} \subseteq \mathbf{V}_1 \vee \mathbf{V}_2 …
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