Math, asked by drbravestone357, 6 months ago

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

Answered by lalithagajelli1969
2

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.

Answered by kmousmi293
0

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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