'Curly' Z and I - Affine algebraic sets

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In summary, the conversation discusses using Latex to produce symbols for subsets and ideals in affine algebraic sets. The notation for a subset Z(S) is represented by a "curly" Z, while the notation for the unique largest ideal is represented by a "curly" I. The conversation also refers to a post on MHF for help with identifying these symbols.
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I am reading Dummit and Foote on affine algebraic sets and wish to create posts referring to such objects.

The notation for a subset Z(S) of affine space is a "curly" Z - see attachment - bottom of page 658.

Also the notion for the unique largest ideal whose locus determines a particular algebraic set V is a 'curly' I - see attachment, third paragraph on page 660.

Can someone please help me to use Latex to produce these symbols.

Peter

[This has also been posted on MHF]
 
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  • #2
\(\mathcal{Z}\)
\(\mathcal{I}\)

Also see the sticky on how to look up symbols.

Code: 
\mathcal{Z}
\mathcal{I}

http://mathhelpboards.com/latex-tips-tutorials-56/need-help-identifying-certain-latex-characters-5223.html
 
  • #3
Thanks dwsmith, ... Appreciate your help

Peter
 

FAQ: 'Curly' Z and I - Affine algebraic sets

What is an affine algebraic set?

An affine algebraic set is a set of solutions to a finite system of polynomial equations with coefficients in a field. In other words, it is the set of points that satisfy a given set of equations.

How is an affine algebraic set related to 'Curly' Z and I?

'Curly' Z and I are symbols used to denote the coordinates of points in an affine algebraic set. These symbols represent the variables in the polynomial equations that define the set.

Can an affine algebraic set have more than one solution?

Yes, an affine algebraic set can have multiple solutions, depending on the equations that define it. The set of solutions can range from finite (a single point) to infinite.

What is the significance of affine algebraic sets in mathematics?

Affine algebraic sets are important in mathematics because they allow us to study and understand the structure of solutions to polynomial equations. They are also used in various areas of mathematics, such as algebraic geometry and commutative algebra.

How do affine algebraic sets differ from other types of algebraic sets?

Affine algebraic sets differ from other types of algebraic sets, such as projective algebraic sets, in terms of the coordinate systems used to define them. Affine algebraic sets are defined using a system of coordinates where each variable represents a distinct dimension, while projective algebraic sets are defined using homogeneous coordinates, which allow for the inclusion of points at infinity.

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