Show that 1+3x is a unit in . Hence, Corollary 4.5 may be false if R is not an integral domain.
It is proved that 1+3x is a unit in .
If any given function R[x] is a ring, then the commutative, associative, and distributive laws hold such that the function f(x)+g(x) exists.
The given unit is 1+3x . The multiplicative inverse of this will be: 1-3x.
Then, we have:
Clearly found to be in .
Hence proved, 1+3x is a unit in .
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