# Tagged Questions

Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

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### Terminology for weighted projective spaces

For a sequence of positive integers $a_1, \ldots, a_n$ and a base ring $R$ there is a graded ring $R[x_1,\ldots, x_n]$ where $x_i$ is in degree $a_i$. We can then apply Proj and get a scheme, and ...
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### Does a plane curve with polar equation $r=\lambda_1\cos^2\theta+\lambda_2\sin^2\theta$ have a name?

Does a plane curve with polar equation $$r=\lambda_1\cos^2\theta+\lambda_2\sin^2\theta$$ where both $\lambda_i>0$ have a name? It's very similar to hippopede, also known as lemniscate of Booth, ...
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### Notation/terminology for “independent” subspaces/subalgebras

Let $V$ denote a vector space (or any other kind of algebraic structure). Question. Letting $I$ denote a fixed set and $X$ denote an $I$-indexed family of subspaces (subalgebras) of $V$, is there ...
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### When do the zero divisors of a commutative ring form an ideal?

Let $J$ denote the set of zero-divisors of a commutative ring $R$. Since we automatically have $RJ \subseteq J$, hence $J$ is automatically halfway to being an ideal. Furthermore, its already "prime",...
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### a new(?) operation using products of multiplicities

Does the operation $$n \odot m := \prod_{p \text{ prime}} p^{v_p(n) \cdot v_p(m)}$$ on positive integers have a common name? Has this operation been studied somewhere? Notice that $\odot$ is ...
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### Definiton of No Tear and No Paste

Topologists often mention an example beginning by "If there is no tear and no paste, then ...". As a student, I am confused with this "term", and I want to know the exact mean of it. First of all, ...
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### Why are centers, centralizers and normalizers called that way?

I know what they are, but where do the names come from?
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### Is there a name for graphs with the following property?

The property of the graph is the following: For any vertex, there is a hamiltonian path starting with this vertex, but the graph is not hamiltonian. The following graph is a small example: ...
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### “Advective”, “diffusive”, “dispersive”, and related terms in the realm of PDEs

Whenever I read a paper involving PDEs, the discussion inevitably refers to “the dispersive term” or “the advective term” or similar. From context it is usually possible to figure out the antecedent, ...
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### Name for a body that can be completely described using its silhouettes

I'm shooting blind over here because I have no background in this field of mathematics. I assume that if you have a body (in $\mathbb{R}^3$), you can call it convex if any segment from one point ...
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### Does this property of scattered spaces have a name?

Let $K$ be a (Hausdorff) scattered topological space and for each ordinal $\alpha$ denote by $K^{(\alpha)}$ the $\alpha$th derivative of $K$ by the Cantor-Bendixson derivation (i.e., define ...
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### Does this operation have a name?

For a field $F$, define the binary operation $\parallel :(F\mathbb{P}^1 \times F\mathbb{P}^1 \setminus\{(0,0)\}) \to F\mathbb{P}^1$ by $$a \parallel b = \frac{1}{\frac{1}{a} + \frac{1}{b}}.$$ This ...
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### What do you call two groups with only trivial homomorphisms between them?

Suppose $G$ and $H$ are groups, and all group homomorphisms $G \to H$ and $H \to G$ are trivial. Is there a common term to describe such a pair of groups with? Like, “$G$ and $H$ are [...]”, or “$G$ ...
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### Is there a name for this graph-theoretic concept?

Let $G$ and $H$ be graphs with vertex sets $V$ and $W$, and $f\colon V \to W$ a function. We say that $f$ preserves $k$-neighborhoods if all points that are at distance $k$ from each other in $G$ are ...
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### Why is recursion theory suffering from terminological bloat?

Several questions on MSE in recent months and most recently this one have made me feel that recursion theory is suffering from terminology bloat. Why have so many synonyms for "recursive" and "...
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### A name for elements of a group generating the same cyclic subgroup

Elements with similar properties usually deserve a name in many contexts, say primitive elements in finite fields, integers modulo a number $n$, generators of a free groups etc. Does there exist a ...
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### In mathematics what does it mean “to occur naturally”?

In mathematics, I often meet the expression " 'x' occurs naturally", or " 'x' occurs naturally in 'Y' ". For example: "You should know why eigenvectors and eigenvalues occur naturally in linear ...
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### Terminology in graph theory

Let $G$ be a finite graph with the following property: For any vertex $a$ and edge $\{b, c\}$ of $G$, there is an edge connecting them: there is one of $\{a,b\}$ or $\{a, c\}$ in $G$. Is there ...
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### Terminology: order vs. degree (in general)

The word degree comes from Latin degradus (through French), which means something like step down. The word order comes from Latin ...
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### In the mean value theorem, we are guaranteed $c$ such that $f'(c) = (f(b)-f(a))/(b-a)$. Does $c$ have a name?

The Mean Value Theorem says approximately that for differentiable $f$, there is a $c \in (a,b)$ such that $$f'(c) = \frac{f(b)-f(a)}{b - a}.$$ I presume that the number $f'(c)$ is the mean value. My ...