If R is a Dedekind domain with quotient field K, F is a finite dimensional extension field
Question:
If R is a Dedekind domain with quotient field K, F is a finite dimensional extension field of K and Sis the integral closure of R in F (that is, the ring of all elements of F that are integral over R), then S is a Dedekind domain.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 40% (5 reviews)
To prove that the integral closure S of a Dedekind domain R in a finitedimensional extension field F of its quotient field K is itself a Dedekind doma...View the full answer
Answered By
User l_998468
I have extensive tutoring experience, having worked as a private tutor for over three years. I have tutored students from different academic levels, including high school, undergraduate, and graduate levels. My tutoring experience has taught me to be patient, attentive to student needs, and effective in communicating difficult concepts in simple terms.
I have a strong background in statistics, probability theory, data analysis, and data visualization. I am proficient in using statistical software such as R, Python, and SPSS, which are commonly used in academic research and data analysis. Additionally, I have excellent communication and interpersonal skills, which enable me to establish rapport with students, understand their learning styles, and adapt my teaching approach to meet their needs.
I am passionate about teaching and helping students achieve their academic goals.
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
-
A valuation domain is an integral domain R such that for all a,b R either a I b or b I a. (Clearly a discrete valuation ring is a valuation domain.) A Prfer domain is an integral domain in which...
-
Let D be a unique factorization domain with a finite number of units and quotient field F. If D[x] has degree n and c o ,c 1 , ... , c n are n + 1 distinct elements of D, then is completely...
-
Let F be an algebraic closure of the field Q of rational numbers and let E F be a splitting field over Q of the set S = { x 2 + a | a Q} so that E is algebraic and Galois over Q (Theorem 3.11). (a)...
-
Provide a brief discussion of database connection using the JDBC API, which includes: a. Two popular methods used to establish a connection b. Operational procedure to establish a connection c. How...
-
Frito-Lay has flourished since its origin-the 1931 purchases of a small San Antonio firm for $100 that included a recipe, 19 retail accounts, and a hand-operated potato ricer. The...
-
How can a local beauty salon store try to generate positive publicity?
-
When heat is transferred by molecular collision, it is referred to as heat transfer by: (a) Conduction (b) Convection (c) Radiation (d) None of these
-
Richardson Company is contemplating the establishment of a share-based compensation plan to provide long-run incentives for its top management. However, members of the compensation committee of the...
-
Take me to the text An employee had $21,800 in gross earnings up to March 20, 2021. She has the following information for her pay for the week ending March 27, 2021. Her employer contributes 100%...
-
Given find the value of b. J3 (2x - 6) dx = 36.
-
If F is a field, then: (a) The ideal (x, y) is maximal in F[x, y]; (b) (x, y) 2 = (x 2 , xy, y 2 ) (c) The ideal (x 2 ,y) is primary and the only proper prime ideal containing it is (x, y)....
-
At the end of 2016 the following information is available for Billings and Phoenix companies: Required a. Prepare a common size income statement for each company. b. Compute the return on assets and...
-
A nearsighted person has a near point of \(20 \mathrm{~cm}\) and a far point of \(40 \mathrm{~cm}\). What refractive power lens is necessary to correct this person's vision to allow her to see...
-
A 3.0-cm-tall object is \(15 \mathrm{~cm}\) in front of a convex mirror that has a \(-25 \mathrm{~cm}\) focal length. Calculate the image position and height.
-
The distance between the objective and eyepiece of a telescope is \(55 \mathrm{~cm}\). The focal length of the eyepiece is \(5.0 \mathrm{~cm}\). What is the angular magnification of this telescope?...
-
A 1.0-cm-diameter microscope objective has a focal length of \(2.8 \mathrm{~mm}\). \(\mathrm{t}\) is used in visible light with a wavelength of \(550 \mathrm{~nm}\). a. What is the objective's...
-
A ray of red light, for which \(n=1.54\), and a ray of violet light, for which \(n=1.59\), travel through a piece of glass. They meet right at the boundary between the glass and the air, and emerge...
-
The enthalpy of vaporization of ethanol is 38.7 kJ/ mol at its boiling point (78oC). Determine Ssys, Ssurr, and Suniv when 1.00 mole of ethanol is vaporized at 78oC and 1.00 atm.
-
Perform the indicated operations. In designing a cam for a fire engine pump, the expression is used. Simplify this expression. (3) (3 4 32
-
Refer to Exercise 3.67. Calculate the coefficient of determination and the least squares line. Is this more informative than the scatter diagram?
-
Compute the coefficient of determination and the least squares line for Exercise 3.64. Compare this information with that developed by the scatter diagram alone.
-
Refer to Exercise 3.59. Compute the coefficients of the least squares line and compare your results with the scatter diagram.
-
Simplify the expression: w+-2w6+ 9 + -w
-
Simplify 343 to the form ab.
-
Divide. 3x r 5 4 Submit your answer in simplified form.
Study smarter with the SolutionInn App