Vipul at 01:51, 4 July 2012

2012-07-04T01:51:59Z

← Older revision		Revision as of 01:51, 4 July 2012
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	# It is the [[localization at a multiplicatively closed subset\|localization]] of <math>R[x]</math> at the multiplicatively closed subset of powers of <math>x</math>.		# It is the [[localization at a multiplicatively closed subset\|localization]] of <math>R[x]</math> at the multiplicatively closed subset of powers of <math>x</math>.
	# It is the ring described as <math>R[x,y]/(xy - 1)</math>.		# It is the ring described as <math>R[x,y]/(xy - 1)</math>.

			==Particular cases==

			* If <math>K</math> is a field, the Laurent polynomial ring <math>K[x,x^{-1}]</math> is an intermediate subring between the polynomial ring <math>K[x]</math> and the [[field of rational functions]] <math>K(x)</math>.

Vipul: Created page with "==Definition== Let $R$ be a commutative unital ring. The '''Laurent polynomial ring''' over $R$ with indeterminate $x$ is denoted $R..."$

2012-07-04T01:38:31Z

Created page with "==Definition== Let <math>R</math> be a commutative unital ring. The '''Laurent polynomial ring''' over <math>R</math> with indeterminate <math>x</math> is denoted <math>R..."

New page

==Definition==

Let <math>R</math> be a [[commutative unital ring]]. The '''Laurent polynomial ring''' over <math>R</math> with indeterminate <math>x</math> is denoted <math>R[x,x^{-1}]</math> and can be defined as follows:

# It is the ring whose elements are <math>R</math>-linear combinations of powers of <math>x</math>, where the exponents are allowed to be integers. Addition is coordinate-wise and multiplication is defined <math>R</math>-linearly so that on powers of <math>x</math> it is defined by adding the exponents.
# It is the [[localization at a multiplicatively closed subset|localization]] of <math>R[x]</math> at the multiplicatively closed subset of powers of <math>x</math>.
# It is the ring described as <math>R[x,y]/(xy - 1)</math>.

Laurent polynomial ring - Revision history

Vipul at 01:51, 4 July 2012

Vipul: Created page with "==Definition== Let R be a commutative unital ring. The '''Laurent polynomial ring''' over R with indeterminate x is denoted R..."

Vipul: Created page with "==Definition== Let $R$ be a commutative unital ring. The '''Laurent polynomial ring''' over $R$ with indeterminate $x$ is denoted $R..."$