prime ideal
A technical term in ring theory: an ideal P such that if a product ab belongs to P, then a or b belongs to P. Used in algebraic number theory and algebraic geometry.
In the ring of integers, an ideal generated by a prime number is a prime ideal.
In commutative ring theory, localization at a prime ideal is an important operation.
From 素 (so, 'prime') + イデアル (idearu, 'ideal'), a direct translation of the English mathematical term 'prime ideal'. The katakana イデアル is a loanword from German 'Ideal' or English 'ideal'.