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冪零元 (べきれいげん) Japanese meaning | Kotomora

冪べき零れい元げん

べ

き

れ

い

げ

ん

Meanings

1

noun

nilpotent element

mathematics

In ring theory, an element x such that x^n = 0 for some positive integer n.

環かんの冪べき零れい元げん全ぜん体たいは冪べき零れい根こん基きをなす。
The set of all nilpotent elements of a ring forms the nilradical.
この行ぎょう列れつ

は

冪べき

零れい

元げん

で

ある

。

This matrix is a nilpotent element.

Written forms

冪べき零れい元げん
Standard kanji form in mathematical contexts.
巾零元べきれいげん
Variant using 巾 instead of 冪; also seen in mathematical writing.

Kanji

冪power, exponent
零zero, spill, overflow
元beginning, former time, origin
巾towel, hanging scroll, width

Similar words

冪べき零れい
冪零 is the adjective 'nilpotent', while 冪零元 specifically refers to a nilpotent element.
冪べき等とう元げん
An idempotent element satisfies x^2 = x, whereas a nilpotent element satisfies x^n = 0.

Etymology

From 冪 (べき, 'power') + 零 (れい, 'zero') + 元 (げん, 'element'). The term is a direct translation of the English 'nilpotent element'.