The intersection of two subrings
(a) is again a subring
(b) can't be a subring
(c) may or may not be a subring
(d) none of these
Answers
Answer:
it's option A ... i.e.., is again a subring
Step-by-step explanation:
The intersection of two subrings is a subring. Proof: Let S1 and S2 be two subrings of ring R. Since 0∈S1 and 0∈S2 at least 0∈S1∩S2.
Answer:
The intersection of two subrings (a) is again a subring
Step-by-step explanation:
A non-empty set R equipped with two binary operations called addition and multiplication denoted by ( + ) and ( • ) is said to be a ring if the following properties hold:
(R,+) is an abelian group.
(R,•) is a semi-group.
(R,+,•) holds distribute law.
a•(b + c) = a•b + a•c
(b + c)•a = b•a + c•a
Subring: A nonempty subset S of a ring R is said to be a subring of R if S forms a ring under the binary operations of R.
• Let (R,+,•) be a ring, Then the nonempty subset S of R is called a subring of R if (S,+,•) is a ring.
• A nonempty subset S of a ring R is said to be a subring of R iff for every a, b ∈ S → ab ∈ S and a - b ∈ S.
Thus, a subring is once again formed at the intersection of the two subrings.
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