Is it possible? [Edit: apart from manually, edge by edge!]
I'm going through a tutorial. The example UV I'm working on is an unwrapped strip from a ball.
Selecting the strip rings (e.g. to straighten them by scaling) proves incredibly challenging! Here's what I tried and didn't work:
1) the select ring function from the 3d view (CtrlAltRMB) doesn't work in UV window
2) using "sync UV with model" gets you the selection from the 3d view but: it'll disappear as soon as you disable sync or it will scale the model you can't scale on "individual origins" if you scale UV edges with sync enabled
3) the Circle or Border selection tools (in UV) do not select in "crossing" mode - i.e. you can't select rings only by drawing a flat narrow selection (you can only select rings AND loops by fatfingering it)
4) the Circle or Border selection tools - if you decide to subract the loops and leave the rings - now, weirdly, will work in "crossing" mode thus subtracting a loop and all your rings from your selection
Alt
+RMB
selects edge loop, while the OP asks for selecting edge ring on UV map. $\endgroup$