Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1) Let R and S be rings. Show that the cartesian product of sets Rx S = {(r,s) |r € R, s E s} with the addition (r, 8) + (r', s') := (r + r', s + s') and the multiplication (r, s) · (r', s') := (r · r', s · s') is a ring.

1) Let R and S be rings. Show that the cartesian product of sets Rx S = {(r,s) |r € R, s E s} with the addition (r, 8) + (r', s') := (r + r', s + s') and the multiplication (r, s) · (r', s') := (r · r', s · s') is a ring.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
1) Let R and S be rings. Show that the cartesian product of sets R x S = {(r, ) |r e R, s €s} with the addition (r, s) + (r', s') := (r +r', s + s') and the multiplication (r, s) · (r', s') := (r - r', s - s') is a ring.
Transcribed Image Text:1) Let R and S be rings. Show that the cartesian product of sets R x S = {(r, ) |r e R, s €s} with the addition (r, s) + (r', s') := (r +r', s + s') and the multiplication (r, s) · (r', s') := (r - r', s - s') is a ring.
Expert Solution
steps

Step by step

Solved in 10 steps with 10 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS