Abstract Algebra: Theory and Applications · Problem SE-1

Polynomials — Thomas Judson

Mathematics — Abstract Algebra · rings-sage

Problem

Define the two rings

\mathbb{Z}_{11}

and

\mathbb{Z}_{12}

with the commands R = Integers(11) and S = Integers(12). For each ring, use the relevant command to determine: if the ring is finite, if it is commutative, if it is an integral domain and if it is a field. Then use single Sage commands to find the order of the ring, list the elements, and output the multiplicative identity (i.e. 1, if it exists).

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