Let R be an integral domain and for each maximal ideal M (which is also prime, of
Question:
Let R be an integral domain and for each maximal ideal M (which is also prime, of course), consider RM as a subring of the quotient· field of R. Show that ∩ RM = R, where the intersection is taken over all maximal ideals M of R.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 45% (11 reviews)
Let R be an integral domain and let M be a maximal ideal of R We have the following inclusion R R...View the full answer
Answered By
Deepak Sharma
0.00
0 Reviews
10+ Question Solved
Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
Question Posted:
Students also viewed these Mathematics questions
-
Find all the second partial derivatives of the function b) f(x,y) = ln(3x + 5y). %3D
-
Proof that Let R be an integral domain with quotient field F. lf T is an integral domain such that R T F, then F is (isomorphic to) the quotient field of T.
-
The Butch Holdings company will pay you $8000 at the end of each year for the next 15 years into an account paying 5% interest. If the first payment is received a year from today, what is the present...
-
The bottle rests at a distance of 3 ft from the center of the horizontal platform. If the coefficient of static friction between the bottle and the platform is s = 0.3m determine the maximum speed...
-
Calculate the 2010 and 2011 MPCs for each of the countries. 2010 2011 AC MPC FRANCE 1,000 EUROS 000 EUROS ITALY BRITAIN 1,000 POUNDS 7,500 PoUNDS RELAND 1,000 EUROS 8000 EUROS 1,000 EUROS 1,000 EURos...
-
Solve the following recurrence relations. a. x(n) = x(n 1) + 5 for n > 1, x(1) = 0 b. x(n) = 3x(n 1) for n > 1, x(1) = 4 c. x(n) = x(n 1) + n for n > 0, x(0) = 0 d. x(n) = x(n/2) + n for n > 1,...
-
When is the assignment of duties among personnel deemed to be compatible? Incompatible?
-
David's Paint Supply experienced the following events during 2012, its first year of operation: 1. Acquired $30,000 cash from the issue of common stock. 2. Purchased inventory for $24,000 cash. 3....
-
How do you define operational excellence? What factors are involved in achieving operational excellence? Who (within an organization) is responsible for operational excellence and why is this...
-
On December 31, the trial balance indicates that the supplies account has a balance, prior to the adjusting entry, of $320. A physical count of the supplies inventory shows that $90 of supplies...
-
Let be the category with objects all commutative rings with identity and morphisms all ring homomorphisms : R S such that {1 R ) = 1 s . Then the polynomial ring Z[x 1 , ... , x n ] is a free...
-
Lagrange's Interpolation Formula. If F is a field, a 0 ,a 1 , ... , a n are distinct elements of F and c 0 ,c 1 , ... , C n are any elements of F, then is the unique polynomial of degree n in F[x]...
-
When glucose, C 6 H 12 O 6 , dissolves in water, which of the following is formed in the solution? (a) Hydrated clusters of H 2 O (b) Hydrated clusters of CO 2 (c) Hydrated clusters of H 2 CO 3 (d)...
-
Suppose that the government introduces a price support for mushrooms and sets the support price at $6 per pound. Who gains and who loses? What are the quantity of mushrooms produced, the surplus, and...
-
Describe the method of allocating table resources in these three restaurants. At McDonalds, no reservations are accepted; at Panorama Restaurant at the St. Louis Art Museum, reservations are...
-
Consider utility functions: with , > 0 and 0 xwith 0 f= E xf f with 0 f Repeat exercise 12.1 Consider the model from section 12.1, where the countries utility functions are: (a) Determine the...
-
Explain how Seattles 20-cents charge will change the use of plastic bags and how the deadweight loss created by plastic bags will change. Plans to curtail use of plastic bags, but not much action...
-
The European Union requires any airline operating to or from an EU airport to participate in the EU cap-and-trade system under which 15 percent of pollution credits for airlines will be auctioned off...
-
Express the quantity 965.33 Cal in joules.
-
Tarick Toys Company manufactures video game consoles and accounts for product costs using process costing. The following information is available regarding its June inventories. The following...
-
What is the sensitivity of the test? Radiology, Cancer A radiologist investigates whether a new (less costly) method for identifying esophageal cancer is as effective as the gold standard. He obtains...
-
Provide a 95% CI for the sensitivity (two decimal place accuracy is sufficient)? Radiology, Cancer A radiologist investigates whether a new (less costly) method for identifying esophageal cancer is...
-
Suppose the probability of an a allele is p. If people mate randomly, then what is the probability of the (aa) genotype? Genetics The estimation of allele probabilities is essential for the closer...
-
A spanning set of linearly independent vectors forms a vector space of dimension =(# of independent vectors). So, if I find 3 independent vectors in R, then the Span(v1, v2, v3) = R 3 3 w=1 Prove =...
-
4. Consider the 8-puzzle problem. The start state and end stats are given in the following: 3 1 2 4 5 6 7 8 1 2 3 4 5 6 7 End state Start state Assume the evaluation function f(n)=g(n)+h(n). Here,...
-
USE THIS FACT PATTERN IN THIS QUESTION: You are a student in a University Business Program. You and two classmates, Rahvie and Patricia, have all developed an idea for a new energy drink specifically...
Study smarter with the SolutionInn App