64 513
Assignments Done
Successfully Done
In September 2018

Answer to Question #44738 in Abstract Algebra for jasvinder

Question #44738

Let S = { matrix [ a 0] | a,b ∈ Z } .
[0 b ]

i) Check that S is a subring of M(subscript2)(R) and it is a commutative ring with identity.
ii) Is S an ideal of M(subscript2)(R)? Justify your answer.
iii) Is S an integral domain? Justify your answer.
iv) Find all the units of the ring S.
v) Check whether
I = { matrix [ a 0] | a,b ∈ Z, 2 | a } .
[0 b]
is an ideal of S.
vi) Show that S is congruent to Z×Z where the addition and multiplication operations are componentwise addition and multiplication.
Expert's answer

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!


No comments. Be first!

Leave a comment

Ask Your question

Privacy policy Terms and Conditions