One of the major aims of invariant principle was to solve the "finite foundation problem". The sum or merchandise of any two invariants is invariant, along with the finite foundation difficulty requested no matter if it absolutely was doable for getting every one of the invariants by starting with a finite listing of invariants, called turbines, after which you can, adding or multiplying the turbines with each other.
All quotient rings of a Noetherian ring are Noetherian, but that doesn't necessarily hold for its subrings. The chain ailment also might be inherited by combinations or extensions of the Noetherian item. For example, finite immediate sums of Noetherian rings are Noetherian, as is the ring of formal electricity sequence about a Noetherian ring.
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