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# Subring R of integral domain D is a subdomain of D.

Modern Algebra
Ring Theory
Subrings
Integral Domain

1) If D is an integral domain and R< = D is a subring of D with unity, show that R is a subdomain of D.
This amounts to showing that 1subR and 1subD are unities from R and D respectively

2) Give an example with D not integral domain where 1subR =/= 1 sub D
(Hint: consider Rsub1 X Rsub2. Warning Rsub1 is not a subring of Rsub1 X Rsub2; it's not even a subset of it)

Note : R <= D means R is a subring of D
1subR means 1 is element of R
1subD means 1 is element of D
Rsub1 mean that R subscrip1
Rsub1 X Rsub2 means cross product.

Modern Algebra
Ring Theory
Subrings
Integral Domain
...

#### Solution Summary

This solution is comprised of a detailed explanation that subring R of integral domain D is a subdomain of D.
It contains step-by-step explanation for the following problem:
1) If D is an integral domain and R< = D is a subring of D with unity, show that R is a subdomain of D.
This amounts to showing that 1subR and 1subD are unities from R and D respectively

2) Give an example with D not integral domain where 1subR =/= 1 sub D
(Hint: consider Rsub1 X Rsub2. Warning Rsub1 is not a subring of Rsub1 X Rsub2; it's not even a subset of it)

Note : R <= D means R is a subring of D
1subR means 1 is element of R
1subD means 1 is element of D
Rsub1 mean that R subscrip1
Rsub1 X Rsub2 means cross product.

Solution contains detailed step-by-step explanation.

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