Polynomial endomorphism IAPS
From Apstheory
Definition
Definition with symbols
Given a ring Failed to parse (Can't write to or create math temp directory): R , the polynomial endomorphism IAPS of Failed to parse (Can't write to or create math temp directory): R
is an IAPS of near-rings whose Failed to parse (Can't write to or create math temp directory): n^{th} member is the endomorphism near-ring of Failed to parse (Can't write to or create math temp directory): R[x_1,x_2,...,x_n] as an Failed to parse (Can't write to or create math temp directory): R
-algebra.
As a functor
The polynomial endomorphism functor is an IAPS functorfrom the category of rings to the category of near-rings. The functor takes in a ring and outputs an IAPS of near-rings.
The unit group functor for this gives the polynomial automorphism IAPS.