If E is a ring of even integers , then show that an ideal  (4) , generateed by 4 is a maximal ideal of E.

Q: Show that A is ideal of A+B? IS an

A: According to questionWe have to show that A is an ideal of A+B

Q: If Z₁2 is a ring under addition and multiplication modulo 12then find its all prime ideals and…

A: If Z12 is a ring under addition and multiplication modulo 12.We have to find its all prime ideals…

Q: Let R be a commutative ring with 1 and I be a proper ideal of R. Prove that I is prime if and only…

A:

Q: K be ideals of a non-commutative division division ring. Then prove or disprove that-I+ K is ideal…

A: (a) Given that I,J,K are ideals of non-commutative division ring. The objective is to show that…

Q: Let R be a commutative ring with unity. Suppose that the only idealsof R are {0} and R. Show that R…

A:

Q: (B) Find all maximal ideals of (Z8, +8,8).

A:

Q: 2. In the ring (4Z, +,.), the ideal (8) is (a) not prime (b) maximal (c) maximal and not prime (d)…

A:

Q: Let T = { | EQ, a and b are relatively prime and 5 does not divide b}. Show that T is a ring under…

A: SOLUTION:  Let T=ab: ab∈ℚ,a and b are relatively prime and 5 does not divide b   We  have  show…

Q: If S be an ideal ofg a ring Z of all integers. Then S is maximal if and only if it is generated by…

A: is an ideal of ring . We have to show if  is maximal if and only if it is generated by some prime…

Q: If S be an ideal ofg a ring Z of all integers. Then S is maximal if and only if it is generated by…

A: If S be an ideal ofg a ring Z of all integers. Then S is maximal if  and only if it is generated by…

Q: Find 5 examples of a ring in which {0R} is maximal

A:

Q: Prove that a finite ring R with unity and no zero divisors is a division ring.

A:

Q: Prove directly that a maximal ideal is irreducible.

A: