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Q: Consider the following closed semi-ring: (R₂ U{+∞o), Min, Max, +∞0, 0) where Min is the operation +…

A: It is given that the closed ring , where Min is the operation + and Max is  an operation.The…

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A: We know that both given ring are field

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A: To define zero divisor and to find whether every ring has zero divisors or not.

Q: Q:- Consider a ving R={o,a,b,c,d, e,f.g} defired by folowing the cayley's tables. elf ef +) a e a d…

A: Solution: The given ring is R=0,a,b,c,d,e,f,g We have to calculate the characteristic of the ring R.

Q: а. Let a, b, c be three elements of a Euclidean ring R and (a, b) = 1. If a/bc then show that a/c.

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

A: Answer

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Q: Q#2 In the ing a unit Z[x1.Show. that is

A: To Show -    Concept used -

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

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Q: Abstract

A: Mn2Z10  for a fixed value of n , say n =2 Consider the ring M2 (2Z10) of 2×2 matrices with the…

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Q: Let a, b e G such that a and b commute, i.e. ab = ba. Note that we are not claiming G is abelian.…

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Q: - show that Zo find the Zero following rings 071 2 78 ax Rings. divisor of Find the Zero divisor of…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: B E None (i), (ii) (iii), (iv) Which of the following are ring homomorphisms? (i): f: (Q(√2), +,-) →…

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Q: Q::Let S1 and S2are two subrings of a ring (R, +,.), prove that S, U S2 is subring of R iff either…

A: 1 Let S1 and S2be two subrings of R,+,.. First suppose that either  S1⊆S2 or S2⊆S1 we will prove…

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Q: Ring theory (abstract algebra)

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Q: The number of idempotents elements in the ring Zg is: 8 O 2 4 1

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Q: -: Define subring. Is the set S is a subring of the ring M %3D Il 2 x 2 matrices?

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Q: The rings Z and 5Z are isomorphic.

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Q: a. Find the elements of Zg that have multiplicative inverses.

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Q: Q1: Find all tHhe idempotent and nilpotent e le ment of the ring Z5

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

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Q: Let R= {0,b,c,d} with operations defined by the tables + 0 c d 0 b C 00 b c d. 0 0 0 0 b 0 0 b b bb…

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Q: Let R be a commutative ring, a, b e R and ab is a zero-divisor. Show that either a or b is a…

A: Given information : Let R be a commutative ring, a,b∈R and abis a zero divisor.

Q: Which of the following elements r of the following rings R are zero divisors? Select all that apply:…

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Q: (R, +, - ) (76,+,. ) Maxi(R), +,) Ring Has identity Commutative E very nonZeru elenet has inverse…

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

A: