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My question is about the terminology or description that specialists in Banach space theory would use to refer to these spaces, when asking each other questions or giving each other outlines of proofs. …

by most readers as saying $H^n(A,M)=0$ for all $n\geq 2$ and all $A$-bimodules $M$ this even has an accepted name ("quasi-free", I think, although corrections are welcome) However, I am looking for terminology … But to my knowledge, although "homology with symmetric coefficients vanishes in all degrees $> n$" clearly has a flavour of being "dimension $\leq n$ in some sense", I don't know of any existing terminology …

So my question is this: do these kinds of algebra have a standard name, and where are the established sources for such terminology? … Rather, I need some idea of whether one choice of terminology is standard, and hence least likely to cause confusion/irritation to the intended audience, should I decide to pursue this course. …

I suspect the answer should be obvious to those who, unlike me, know some basic Lie group/Lie algebra terminology. …

This question has a subjective component but I would like answers that try to stick to concrete observable facts, such as which papers use which terminology. … My question is this: is there a current consensus on which terminology to use? …

Is there standard notation or terminology for functions $\theta:R\to S$ that satisfy $$\theta(ar)=\theta(a)\theta(r) \quad,\quad \theta(rb)=\theta(r)\theta(b) \quad\hbox{for all $a,b\in D$ and all $r\in … Note that I am not really asking for people's opinions on inventing new terminology, but checking among the research community if there is an existing accepted name for these objects, which my coauthors …

Fix an odd prime power $q$, fix a generator of the multiplicative group ${\mathbb F}_q^\times$, let $H$ be the subgroup generated by the square of this element, and form the semi-direct product ${\mat …

Fix a unital commutative ring $R$ and consider a left $R$-module $M$. $\newcommand{\End}{{\rm End}}$ (For the indirect application I have in mind, which would require another post, $\End_R(M)$ will n …

Is the terminology used in Bollobas's book now the standard one? If so, have people seen the notion of "subtrace" before? … So my question is really about whether traces and subtraces are just as standard, or whether this is a convenient bit of terminology popular within a particular cluster of researchers. …

To be specific: if $G$ is a finite group and $\operatorname{Irr}(G)$ the set of its irreducible characters (over the complex field) then we know that $$ 1 = \sum_{\phi \in {\rm Irr}(G)} \frac{(d_\phi) …

The terminology is my own, because I don't know if there is existing terminology that I should be using instead. …