#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## or

There is no recursive or definable R such that......

If...... then R is right Noetherian provided R is semiprime [2] or
commutative [4] or R/N has zero socle.

The case when f is decreasing can be proved similarly, or else can
be deduced from......

Then f=g, or equivalently a(f)=a(g).

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