{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

st21 - S-1 R if and only if S ∩ M =/0(17 points 3 Let R...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 5125 Monday, October 24 Sample Second Test no. 1. Answer All Problems. Please Give Explanations For Your Answers. 1. Let R be a commutative ring and let I denote the set of nilpotent elements of R (that is, { r R | r n = 0 for some positive integer n } ). Prove that I ± R and that R / I has no nonzero nilpotent elements. (16 points) 2. Let R be a commutative ring, let M be a maximal ideal of R , and let S be a multiplica- tively closed subset of R which contains 1. Prove that S - 1 M is a maximal ideal of
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: S-1 R if and only if S ∩ M = /0. (17 points) 3. Let R be a UFD. Prove that R [ x ] has infinitely many irreducible elements, no two of which are associates. (17 points) Test on Wednesday, November 2. Material Chapters 7,8,9 approximately. One of the problems will be identical to one of the ungraded homework problems and one of the problems will be identical to one of the sample test problems....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online