Polynomial endomorphism IAPS

From Apstheory

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Current revision as of 14:54, 30 December 2006

[edit] Definition

[edit] 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.

[edit] 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.