Science Quiz / Modern Algebra Rings

Random Science or Math Quiz

Can you name the Properties of Rings?

 Plays Quiz not verified by Sporcle

How to Play
Support Sporcle.
Go Orange.
Score 0/47 Timer 20:00
Idea or QuestionExample or DefintionExtra Information
1. What are the properties of a Ring?
Example of infinite Commutive Ring with only one unity:
Example of infinite Commutive Ring without unity:
If a ring has a unity, or a ring element has a mulitplicative inverse, then ___________?
5. S is a Subring of R if __________ ?
Subring Test:
Find all subrings of Z12:
Find all subrings of Z12:
Find all subrings of Z12:
10. Find all subrings of Z12:
Find all subrings of Z12:
Definition of Zero-Divisors: (equation)
Definition of Integral Domain:
15. Zn is an Integral Domain when _________ ?
Is QxQ an Integral Domain?
Definition of Field:
In a finite set what's the difference between integral domain and a field?
Consequence of Questions 15 and 18.
20. What are the elements of Z3[i]?
Solve x^3 + 2 = 0 in Z3[i]. (Just solution set {a,b,c}
If nx = 0 for all x in R, then n is __________
The characteristic of R is ___________
The characteristic of an ID is __________
Idea or QuestionExample or DefintionExtra Information
25. If for all r in R, a in A, ra and ar are in A, then A is _________?
Ideal Test:
Let I = (a1, a2), then I is __________ ?
R/A is a factor ring if and only if
If ab in A implies a in A or b in A, then A is __________?
30. If A is an Ideal with no proper Ideal containing it, then A is ___________?
R/A is an ID if and only if
R/A is an field if and only if
Let f:R to S, with f(a+b) = f(a)+f(b), and f(ab) = f(a)f(b), then f is _________?
If f is bijective it is __________?
35. Under homomorphisms Kernels are ______?
Let f:R to S be a ring homomorphism. Then R/Ker(f) is isomorphic to f(R), by r + Ker(f) ---> f(r).
Let f: R --> R/A, by f(r) = r + A. This shows ________
If D[x] is not an integral domain, then
In F[x], with functions f,g then there exists unique functions q,r such that f = gq + r, and _____________
40. Let F be a field, a in F, f(x) in F[x]. Then f(a) is ____
If f(a) = 0, then
Polynomials of degree n have _______
Let x^k - 1 = 0. Then w = e^(2*pi*i/k) is called _______
If every ideal has the form (a) = {ra | r in R}, the R is a _________
45. Let F be a field, then F[x] is ___________
I = (g(x)) if and only if ________
x^2 - 4 / x + 2 in Z5[x] , Find q(x) and r(x)

You're not logged in!

Compare scores with friends on all Sporcle quizzes.
Log In

From the Vault

Capitals of the World (Multiple Choice)

by Eobo

Get ready for a multiple choice marathon!
Remove Ads.
Support Sporcle.
Get the best of Sporcle when you Go Orange. This ad-free experience offers more features, more stats, and more fun while also helping to support Sporcle. Thank you for becoming a member.

Show Comments


Created Feb 20, 2011ReportNominate
Tags:Math Quiz, algebra

Top Quizzes Today

Score Distribution

Your Account Isn't Verified!

In order to create a playlist on Sporcle, you need to verify the email address you used during registration. Go to your Sporcle Settings to finish the process.

Report this User

Report this user for behavior that violates our Community Guidelines.