Abstract Algebra: Theory and Applications · Problem 36

Polynomials — Thomas Judson

Mathematics — Abstract Algebra · direct-product-rings

Problem

Let RR and SS be arbitrary rings. Show that their Cartesian product is a ring if we define addition and multiplication in R×SR \times S by (a) (r,s)+(r′,s′)=(r+r′,s+s′)(r, s) + (r', s') = (r + r', s + s') (b) (r,s)(r′,s′)=(rr′,ss′)(r, s)(r', s') = (rr', ss')

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