All Questions
Tagged with universal-algebra terminology
12 questions
2
votes
0
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128
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What is the name of the largest subobject where a map is equivariant?
Suppose we have two objects $X,Y$ with a $G$-operation and a non-equivariant map between them. In this situation, we can look at the largest subobject $X'$ of $X$ on which $f$ is $G$-equivariant.
Is ...
- 11.1k
4
votes
2
answers
236
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Presentationally finite group "extensions"
Fix a group $G$ and fix a presentation of $G$ as $\langle X\mid R\rangle$. A presentationally finite extension of $G$ is any group that can be presented as $H=\langle X\cup X'\mid R\cup R'\rangle$, ...
- 1,338
0
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3
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139
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value (element of an algebra), constant, variable, ground and non-ground terms, free algebras : there is a need for clarification
I have been developing an algorithm to compute the congruence defined by a finite set of "generators" and a finite set of equations (in the sense of equational theories). The algorithm ...
6
votes
2
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457
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Name of a group-like structure
The late Vladimir Arnold, in
Arnold, V., Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world, Bull. Braz. Math. Soc. (N.S.) 34, No. 1, ...
- 2,901
2
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115
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Name for generalization of property: $f^n(x) \ne x$ for all $n > 0$
I am curious about how to specify with standard terminology that a certain function is non-periodic, in the following sense:
In the simple case of a unary operation $f: X \to X$, this property would ...
- 193
2
votes
1
answer
302
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Name for this algebraic structure?
I've found myself looking at a structure $\mathbb{M}$ whose important properties are:
$\mathbb{M}$ is a discretely ordered additive monoid.
$\mathbb{M}$ has a least element, and this least element is ...
- 10.1k
4
votes
1
answer
434
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Regarding a new algebraic structure
By "left semigroup-joined-semigroup" I mean an algebraic structures $(S,\cdot,*)$ such that both $\cdot,*$ are associative, and the following property holds (see this )
$$
x*(y\cdot z)=x*y*z\;\; ; \;...
- 995
1
vote
0
answers
142
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A generalization of quasi-identities
In universal algebra, a variety is axiomatized by identities $t \approx s$ between terms $t$ and $s$. More general are quasi-varieties that are axiomatized by quasi-identities of the form $$u_1 \...
- 44.4k
3
votes
1
answer
297
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What to call substructures in universal algebra in which we restrict the signature?
Suppose $\Sigma$ is a signature in the sense of universal algebra and $\Sigma' \subseteq \Sigma$ a sub-signature. Every $\Sigma$-algebra is also a $\Sigma'$-algebra in a forgetful way. Suppose $A$ is ...
- 48.8k
8
votes
0
answers
619
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The name for a partial order
In a recent paper of mine, my co-authors found that a partial order that we were using was contained in a paper by Kundgen. In it, he called it "right-shifted partial order". I was curious, and found ...
- 4,636
13
votes
3
answers
8k
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$fgf = f$, $gfg = g$, $fg$ not necessarily identity, what is this called?
A very simple question, I just totally forgot how it was called, and Google is not helping.
There's a pair of functions $f:X\to Y$, $g:Y\to X$.
$fgf = f$, $gfg = g$, but $fg$ and $gf$ don't need to ...
- 241
6
votes
3
answers
487
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Terminology: Name for a homomorphism from the free object?
Is there a standard name for taking a homomorphism from the free object over an algebraic structure? Roughly speaking, this should amount to evaluation of any element of the free object under the ...
- 63