I'm trying to figure out how to pronounce the symbols $\oplus,\otimes,\rtimes,\cup$, and $\cap$ when they're being used as binary operators in the contexts of direct sums, tensor products, semidirect products, unions, and intersections, respectively.
I was noticing that we can read aloud $a + b$ either as the sum of $a$ and $b$ or as $a$ plus $b$, and likewise we can read aloud $a\times b$ as the product of $a$ and $b$ or as $a$ times $b$.
However, I've only read that I should pronounce:
$A\oplus B$ as the direct sum of $A$ and $B$,
$A\otimes B$ as the tensor product of $A$ and $B$,
$A\rtimes B$ as the semidirect product of $A$ and $B$
$A\cup B$ as the union of $A$ and $B$, and
$A\cap B$ as the intersection of $A$ and $B$.
I'm wondering: are there similar alternatives for how to say the above expressions in the form "$A$ [name of binary operator] $B$"? Obviously I can pronounce them using their standard LaTeX symbol names, but I was wondering if there were other alternatives? As an example, one of my professors pronounces $A\otimes B$ as $A$ tensor $B$ (he doesn't say $A$ otimes $B$), but I wasn't sure if that was common or just his own habit.
"$A$ cup $B$" and "$A$ cap $B$" are standard for union and intersection. "$A$ tensor $B$" is common for the tensor product. I have never heard anyone use a short name for direct sum or semidirect product or use "oplus" or "otimes" other than when referring to the $\LaTeX$ macros.