Iffis a ring homomorphism from Zm to Zn such that f (1) = b, then bak+2 = bk. True O False

Q: If fis a ringhomomorphism from Zm to Zn such thatf(1) = b, then bak+2 = bk. True False

A: given a ring homomorphism.

Q: The function p: Zs → Z30 defined by ø(a) = 6a is a ring homomorphism. True False

A:

Q: Let R be a ring with unity. Show that (a) = { £ xay : x, y e R }. finite

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Q: If fis a ring homomorphism from Zm to Zn such that f (1) = b, then b4k+2 = bk True False

A:

Q: Q2) Let (M₂ (R), +..) be a ring. Prove H = {(a) la, b, c €. = {(ab)la, b, c € R}is a subring of (M₂…

A: Subring Test : A non empty subset S of a ring R is a subring if S is closed under subtraction and…

Q: Let S be a ring. Determine whether S is commutative if it has the following property: whenever æy =…

A:

Q: If Ø: R → S is a ring homomorphism. The Ø preserves: Nilpotent elements O Idempotent elements O…

A:

Q: Let R be a ring with unity 1 and char (R) = 3. Then R contains a subring isomorphic to

A: Let R be a ring with unity 1 and char(R)=3.  Then R contains a subring isomorphic to_______.

Q: Q:Let S and Szare two subrings of a ring (R, +..), prove that S, US2 subring of R iff either S, C S…

A:

Q: If fis a ring homomorphism from Zm to Z, such that f(1)= b, then b**2 = b*. True False

A:

Q: Let R = Q[V2] and S = Q[V3]. Show that the only ring homomorphism from R to S is the trivial one. In…

A:

Q: - Prove that, if I is an ideai of the ring Z of integer numbers then I=, for some nɛZ'U{0}

A:

Q: Iffis a ring homomorphism from Zm to Zn such thatf(1) = b, then bak+2 = bk. True False

A: Ring homorphism

Q: If R is a commutative ring and Ø:R→S is a ring homomorphism, then S is a commutative ring True O…

A:

Q: If fis a ring homomorphism from Zm to Z, such that f (1)= b, then b4k+2 = bk. %3D O True O False

A:

Q: If Ø: R → S is a ring homomorphism. The Ø preserves: All of these Nilpotent elements Units O…

A:

Q: 1- Let ý:R, » R, be a ring homomorphism such that Kerø =. Then, o is a) 1-1 b) onto c) Both 1-1 and…

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Q: If Ø: R → S is a ring isomorphism. The Ø preserves: O Nilpotent elements Units Idempotent elements O…

A:

Q: - The mapping f: Z → Z defined by f (n) = 5n is a ring homomorphism. a) True b) False

A:

Q: 1- Let ý:R, » R, be a ring homomorphism such that Kerø = . Then, ø is a) 1-1 b) onto c) Both 1-I and…

A:

Q: Let S be a ring. Determine whether S is commutative if it has the following property: whenever ry =…

A:

Q: If R is a commutative ring with unity and a e R, then (a) = {ar:reR}=aR. %3D %3D

A:

Q: If N is an ideal of a ring R, which of the following statements is NOT always true? N is a subring…

A: Given : N is an ideal of a ring R

Q: If Ø: R → S is a ring homomorphism. The Ø p O Idempotent elements Units All of these Nilpotent…

A: For a ring R, the element a∈R is idempotent if a2=a For a ring R, the element a∈R is nilpotent if…

Q: * (7 If f:(R.+)- (R', +' be a ring Homomorphism, and R is integral domain, then R' is integral…

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Q: Let R, , O is a ring under two composion e and O üs follows ü e i; = a + b + 1 and aOb = ab + a + b…

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Q: If f is a ring homomorphism from Z„ to Z„ such that f (1) = b, then b4*+2 = b*. O True False

A: Given f : Zm→Zn is a ring homomorphism such that f1=b Here, we have to check whether b4k+2=bk is…

Q: A ring, R, in which r^2 = r for all elements r in R is called a Boolean ring. In any Boolean ring,…

A:

Q: If fis a ring homomorphism from Zm to Z, such that f (1) = b, then b*+2 = b*. True False

A:

Q: Q1: Let S, and Szare two subrings of a ring (R, +,.), prove that S, USz is subring of R iff either…

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Q: The ring 5Z is isomorphic to the ring 6Z True O False

A:

Q: Q2: Let X be anon-empty set, prove that (p(X), An) is ring?

A:

Q: Iffis a ring homomorphism from Zm to Zn such thatƒ(1) = b, then b4k+2 = bk. %3D True False

A:

Q: 35. Show that the first ring is not isomorphic to the second. (a) Eand Z © Z × Zu and Z () ZXZ, and…

A: The objective is to show that the first ring of the following is not isomorphic to the second:

Q: - The mapping f:Z → Z defined by f (n) = 5n is a ring homomorphism. a) True b) False

A:

Q: Q: Let S, and Szare two subrings of a ring (R, +,.), prove that S, US2 is subring of R iff either S,…

A: By supposinɡ S1 and S2 as two subrinɡs of rinɡ (R, +, .) To prove that S1∪ S2 is subrinɡ of R if and…

Q: Iff is a ring homomorphism from Zm to Zn such thatf(1) = b, then bak+2 = bk . O True O False

A: False

Q: Q: Let S, and Szare two subrings of a ring (R, +,.), prove that S, USz is subring of R iff either S,…

A: I jave used the definition of subring

Q: Let A, B,C be rings. Let & be a ring homomorphism from A into B and ß be a ring homomorphism from B…

A:

Q: If R is a commutative ring and Ø:R→S is a ring homomorphism, then S is a commutative ring * O True O…

A:

Q: Iffis a ring homomorphism from Zm to Zn such that f(1) = b, then b4k+2 = bk. True False

A:

Q: Iff is a ring homomorphism from Zm to Zn such that f (1)=b, then b*+2 = b*. False True

A:

Q: The map f: Z→ Z,o given by f(x)= 2x is a ring homomorphism. Select one. True False

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: 1. Suppose that p: R → S is a ring homomorphism and that the image of o is not {0}. If R has a unity…

A:

Q: 4 The correspondence ø:x > 5x from Z, to Z, is a ring homomorphism. a) True b) False O a) True O b)…

A:

Q: If µ is finitely additive on a ring R; E, F eR show µ(E) +µ(F) = µ(Eu F)+µ(En F) %3D

A:

Q: (b) Show that if : R→ S is only assumed to be a ring homomorphism, then it is possible to have a…

A: We can prove the above result using two contradictory examples. Note that these examples are only…

Q: Show that a ring R is commutative if and only it a - b = (a+ b) (a - b) for all a, be R.

A: Proof. Let R be commutative. Then ab = ba for all a,b ∈ R.

Q: Va, beZatb = a + b +2 and aob = a tabtb is a Ring!

A:

Q: If Ø: R → S is a ring homomorphism. The Ø preserves: Units All of these Nilpotent elements…

A: The units in a ring are those elements which have an inverse under multiplication. An element x of…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.