Polynomial ring: Difference between revisions

Revision as of 08:58, 8 August 2007

Definition for commutative rings

Definition with symbols

Let $R$ denote a commutative unital ring. The, the polynomial ring over $R$ in one variable, denoted as $R[x]$ where $x$ is termed the indeterminate, is defined as the ring of formal polynomials in $x$ with coefficients in $R$ .

Functoriality

The map sending a commutative unital ring to its polynomial ring is a self-functor on the category of commutative unital rings.

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 ===Definition with symbols===
-Let <math>R</math> denote a [[commutative unital ring]]. The, the polynomial ring over <math>R</math> in one variable, denoted as <math>R[x]</math> where <math>x</math> is termed the ''indeterminate'', is defined as the ring of formal polynomials in <math>x</math> with coefficients on <math>R</math>.
+Let <math>R</math> denote a [[commutative unital ring]]. The, the polynomial ring over <math>R</math> in one variable, denoted as <math>R[x]</math> where <math>x</math> is termed the ''indeterminate'', is defined as the ring of formal polynomials in <math>x</math> with coefficients in <math>R</math>.
 ==Functoriality==