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Definition df-chr 19977
Description: The characteristic of a ring is the smallest positive integer which is equal to 0 when interpreted in the ring, or 0 if there is no such positive integer. (Contributed by Stefan O'Rear, 5-Sep-2015.)
Assertion
Ref Expression
df-chr chr = (𝑔 ∈ V ↦ ((od‘𝑔)‘(1r𝑔)))

Detailed syntax breakdown of Definition df-chr
StepHypRef Expression
1 cchr 19973 . 2 class chr
2 vg . . 3 setvar 𝑔
3 cvv 3304 . . 3 class V
42cv 1595 . . . . 5 class 𝑔
5 cur 18622 . . . . 5 class 1r
64, 5cfv 6001 . . . 4 class (1r𝑔)
7 cod 18065 . . . . 5 class od
84, 7cfv 6001 . . . 4 class (od‘𝑔)
96, 8cfv 6001 . . 3 class ((od‘𝑔)‘(1r𝑔))
102, 3, 9cmpt 4837 . 2 class (𝑔 ∈ V ↦ ((od‘𝑔)‘(1r𝑔)))
111, 10wceq 1596 1 wff chr = (𝑔 ∈ V ↦ ((od‘𝑔)‘(1r𝑔)))
Colors of variables: wff setvar class
This definition is referenced by:  chrval  19996
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