Is ℤ3 a Subring of ℤ? Understanding the Mathematical Relationship

Bachelier · Oct 4, 2011

By the way ℤ3 (or ℤ/3ℤ) (mod 3) is not a subring of ℤ, is it?

thanks

lavinia · Oct 4, 2011

Bachelier said:

By the way ℤ3 (or ℤ/3ℤ) (mod 3) is not a subring of ℤ, is it?

thanks

no. Z3 is torsion, Z is free. Z3 is a quotient ring of Z by 3Z.

Bacle · Oct 4, 2011

These are different types of objects, Bachelier; Z/3 is a set of equivalence classes, and Z is a collection of numbers. If maybe you mean whether Z/3 can be embedded in Z as a subring, the answer is no, by, e.g., Lavinia's argument.

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