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Definition df-lnr 40052
Description: A ring is left-Noetherian iff it is Noetherian as a left module over itself. (Contributed by Stefan O'Rear, 24-Jan-2015.)
Assertion
Ref Expression
df-lnr LNoeR = {𝑎 ∈ Ring ∣ (ringLMod‘𝑎) ∈ LNoeM}

Detailed syntax breakdown of Definition df-lnr
StepHypRef Expression
1 clnr 40051 . 2 class LNoeR
2 va . . . . . 6 setvar 𝑎
32cv 1537 . . . . 5 class 𝑎
4 crglmod 19934 . . . . 5 class ringLMod
53, 4cfv 6324 . . . 4 class (ringLMod‘𝑎)
6 clnm 40017 . . . 4 class LNoeM
75, 6wcel 2111 . . 3 wff (ringLMod‘𝑎) ∈ LNoeM
8 crg 19290 . . 3 class Ring
97, 2, 8crab 3110 . 2 class {𝑎 ∈ Ring ∣ (ringLMod‘𝑎) ∈ LNoeM}
101, 9wceq 1538 1 wff LNoeR = {𝑎 ∈ Ring ∣ (ringLMod‘𝑎) ∈ LNoeM}
Colors of variables: wff setvar class
This definition is referenced by:  islnr  40053
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