322second99 - Name : Surname : (5) Let A , B be felds and...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 322 Second Midterm Examination Name: May 18, 1999 Signature : 9:30–11:00 (1) Is Q ( 3 + 5 + 7) = Q ( 3 , 5 , 7)? Why or why not? (10 points)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
(2) Find | Q ( 3 + 5) : Q ( 3) | . Justify your answer. (15 points)
Background image of page 2
Name : Surname : (3) Find the number of irreducible monic polynomials of degree 36 in F 3 [ x ], and in F 5 [ x ]. (15 points)
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
(4) Construct a feld in which x 2 + x + 1 F 5 [ x ] has a root. Describe its ele- ments, explain how addition and multiplication are carried out and how inverses oF nonzero elements are Found. (20 points)
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Name : Surname : (5) Let A , B be felds and let C be a division ring such that A ⊆ B ⊆ C , so that C is a vector space over A and over B , and B is a vector space over A . Suppose that dim A B = s ∈ N and dim B C = r ∈ N . Is it true that dim A C = rs ? (20 points) (6) Let K , E be felds and let D be an integral domain such that K ⊆ D ⊆ E . IF E is algebraic over K , does it necessarily Follow that D is a feld? (20 points)...
View Full Document

This note was uploaded on 11/08/2011 for the course MATH 331 taught by Professor Talinbudak during the Spring '11 term at Boğaziçi University.

Page1 / 6

322second99 - Name : Surname : (5) Let A , B be felds and...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online