Let R be a Boolean ring with more than 2 elements. Find all Divisors of R.

Question

Question

$Let \ R \ be \ a \ Boolean \ ring \ with \ more \ than \ 2 \ elements. \ Find \ all \ Divisors \ of \ R.$

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Byfes * First note the following definitions as 0. Beclean Ringest is a ring for which x² = x V XAR. Zero diursors a, b are s =) every non-o& non unit element is a zero divisos Hence, Divisors of a R1 {0, 1} And CS Scanned with CamScanner

The answer is in the pic. If any doubt still remained, let me know in the comment section.

If this solution helped, please don't forget to upvote to encourage us. We need your support. Thanks ☺☺☺ :)

Add a comment

Answer 2

Similar Homework Help Questions

Consider the ring Z/10Z. Choose for all of the elements whether they are zero-divisors, units, both,...

Consider the ring Z/10Z. Choose for all of the elements whether they are zero-divisors, units, both, or none of them 0 is Select] Select] 2 is Select 3 is Select Let's skip some now and do 8 is ISelect ] 9 is Select
find the three zero divisors in the ring M_2(Z3)

find the three zero divisors in the ring M_2(Z3)
Let R be a commutative ring with no nonzero zero divisor and elements r1,r2,.. . ,Tn where n is a...

Let R be a commutative ring with no nonzero zero divisor and elements r1,r2,.. . ,Tn where n is a positive integer and n 2. In this problem you will sketch a proof that R is a field (a) We first show that R has a multiplicative identity. Sinee the additive identity of R is, there is a nonzero a E R. Consider the elements ari, ar2, ..., arn. These are distinct. To see O. Since R conelude that0, which...

Problem 4. (i) Let R> 2/14Z and consider the polynomial ring R[d]. Let A(z) 4 +...

Problem 4. (i) Let R> 2/14Z and consider the polynomial ring R[d]. Let A(z) 4 + 2r3 + 3r2 + 4x + 5 and B(x) 37 be elements of R]. Find q(x) and r(x) in R] such that: A(x)-q(z)E(z) + r(z) and deg(r) < 2. (2pts) (ii) Let R- Z/11Z, write down the table of squares in R as follows. For every a E R (there are 11 such elements), find a2. Here you are required to express the final...
) Find an example of a commutative ring R with elements 1,7 € R such that...

) Find an example of a commutative ring R with elements 1,7 € R such that (1) = (y), but I and y are not associates.
) Find an example of a commutative ring R with elements 1,7 € R such that...

) Find an example of a commutative ring R with elements 1,7 € R such that (1) = (y), but I and y are not associates.

) Find an example of a commutative ring R with elements 1,7 € R such that...

) Find an example of a commutative ring R with elements 1,7 € R such that (1) = (y), but I and y are not associates.
(6) Let R be a commutative ring. For elements r, s є R, prove the Binomial Theorem in R: Here if ...

Abstract Algebra (6) Let R be a commutative ring. For elements r, s є R, prove the Binomial Theorem in R: Here if n Z, r є R, we interpret nr to be the element in R which is a sum f n many r's. (6) Let R be a commutative ring. For elements r, s є R, prove the Binomial Theorem in R: Here if n Z, r є R, we interpret nr to be the element in R...
Let R be a commutative ring which has exactly four ideals {0}, I, J, and R....

Let R be a commutative ring which has exactly four ideals {0}, I, J, and R. Among all such rings find a ring which has the smallest number of elements.

Problem 4. (i) Let R> 2/14Z and consider the polynomial ring R[d]. Let A(z) 4 + 2r3 + 3r2 + 4x + ...

Problem 4. (i) Let R> 2/14Z and consider the polynomial ring R[d]. Let A(z) 4 + 2r3 + 3r2 + 4x + 5 and B(x) 37 be elements of R]. Find q(x) and r(x) in R] such that: A(x)-q(z)E(z) + r(z) and deg(r) < 2. (2pts) (ii) Let R- Z/11Z, write down the table of squares in R as follows. For every a E R (there are 11 such elements), find a2. Here you are required to express the final...

Let R be a Boolean ring with more than 2 elements. Find all Divisors of R.

Homework Answers

Add Answer to:
Let R be a Boolean ring with more than 2 elements. Find all Divisors of R.

Post as a guest

Earn Coins

Consider the ring Z/10Z. Choose for all of the elements whether they are zero-divisors, units, both,...

find the three zero divisors in the ring M_2(Z3)

Let R be a commutative ring with no nonzero zero divisor and elements r1,r2,.. . ,Tn where n is a...

Problem 4. (i) Let R> 2/14Z and consider the polynomial ring R[d]. Let A(z) 4 +...

) Find an example of a commutative ring R with elements 1,7 € R such that...

) Find an example of a commutative ring R with elements 1,7 € R such that...

) Find an example of a commutative ring R with elements 1,7 € R such that...

(6) Let R be a commutative ring. For elements r, s є R, prove the Binomial Theorem in R: Here if ...

Let R be a commutative ring which has exactly four ideals {0}, I, J, and R....

Problem 4. (i) Let R> 2/14Z and consider the polynomial ring R[d]. Let A(z) 4 + 2r3 + 3r2 + 4x + ...

Let R be a Boolean ring with more than 2 elements. Find all Divisors of R.

Homework Answers

Add Answer to: Let R be a Boolean ring with more than 2 elements. Find all Divisors of R.

Post as a guest

Earn Coins

Add Answer to:
Let R be a Boolean ring with more than 2 elements. Find all Divisors of R.