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Feb 24, 2018 at 22:44 comment added Jesse Elliott Agreed it's partial, but it was too long to include just as a comment. I characterized the $J$ for which there can be no $a$ in $J^r \backslash J$.
Feb 24, 2018 at 14:58 comment added მამუკა ჯიბლაძე Nice answer but partial: OP asks about conditions both on $a\in R$ and/or $J$ which would ensure that $a$ cannot lie in $J^r\setminus J$.
Feb 24, 2018 at 11:25 history edited Jesse Elliott CC BY-SA 3.0
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Feb 24, 2018 at 11:13 history edited Jesse Elliott CC BY-SA 3.0
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Feb 24, 2018 at 10:49 history answered Jesse Elliott CC BY-SA 3.0