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Definition df-lnr 27293
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  e.  Ring  |  (ringLMod `  a )  e. LNoeM }

Detailed syntax breakdown of Definition df-lnr
StepHypRef Expression
1 clnr 27292 . 2  class LNoeR
2 va . . . . . 6  set  a
32cv 1652 . . . . 5  class  a
4 crglmod 16243 . . . . 5  class ringLMod
53, 4cfv 5456 . . . 4  class  (ringLMod `  a
)
6 clnm 27152 . . . 4  class LNoeM
75, 6wcel 1726 . . 3  wff  (ringLMod `  a
)  e. LNoeM
8 crg 15662 . . 3  class  Ring
97, 2, 8crab 2711 . 2  class  { a  e.  Ring  |  (ringLMod `  a )  e. LNoeM }
101, 9wceq 1653 1  wff LNoeR  =  {
a  e.  Ring  |  (ringLMod `  a )  e. LNoeM }
Colors of variables: wff set class
This definition is referenced by:  islnr  27294
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