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Results tagged with universal-algebra
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user 43439
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).
4
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1
answer
171
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A question regarding equational bases of the theory of the commutative and associative prope...
Suppose we are working in the language of a binary operation symbol $*$. Let $S$ be a set of equations which generate precisely the same equational theory generated by the set containing the commutati …
- 2,013
1
vote
1
answer
62
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Follow up to a question on equational bases of the theory of the commutative and associative...
This is a natural follow-up to my previous question, here: A question regarding equational bases of the theory of the commutative and associative properties. As before, suppose we are working in the s …
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2
votes
0
answers
170
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Are there two equations with no equation strictly between them, but at least one quasi-equat...
I asked this question on Math Stack Exchange a while ago, but no one has responded yet. So, I am asking it here. Consider the signature of a single binary operation $+$, and consider the set $Eq$ of a …
- 2,013
17
votes
2
answers
3k
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Is there an identity between the associative identity and the constant identity?
This is a follow-up to my previous question, here: Is there an identity between the commutative identity and the constant identity?. Let our signature be that of a single binary operation $+$. I defin …
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26
votes
2
answers
3k
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Is there an identity between the commutative identity and the constant identity?
I asked this on Math Stack Exchange, but it didn't get a single answer. So, I am now asking it here. Let our signature be that of a single binary operation $+$. I define the constant identity to be $x …
- 2,013
1
vote
0
answers
82
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Equational identities of unordered $n$-tuples
I asked this question on math stack exchange, but I did not get an answer, so I am asking it here. This question combines both universal algebra and set theory. Let $V$ be a model of ZFC set theory, l …
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7
votes
1
answer
322
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Is the partial order of all equations in the signature of magmas a lattice?
$\newcommand\Eq{\mathrm{Eq}}$I asked this question on math stack exchange, here, but there were no comments or answers. So, I am asking it here on mathoverflow. Consider the signature of a single bina …
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13
votes
0
answers
229
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Is there a finite equational basis for the join of the commutative and associative equations?
I asked this on math stack exchange, but I was told to post it on mathoverflow. Consider the lattice of equational theories of a single binary operation $*$. The meet of the theory axiomatized by the …
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5
votes
3
answers
576
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Is the class of power-associative binars finitely axiomatizable?
A binar is simply a set $S$ equipped with a single binary operation $*$. A power-associative binar is a binar where the subalgebra generated by a single element is associative. Equivalently, they can …
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10
votes
0
answers
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Equational theory in the signature (+,*,0,1) of sedenions and beyond
Consider a Cayley-Dickson algebra $(X,+,∗,0,1)$, that is an algebra generated from the reals by the Cayley-Dickson construction. From complexes to quaternions, we lose commutativity of multiplication, …
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8
votes
2
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Is the equational theory of groups axiomatized by the associative law?
Consider the class of groups in the signature {*}. Is the equational theory of that class axiomatized by the associative law? I asked this on math stack exchange but I didn't receive a satisfactory an …
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