MATH 417 Study Guide - Midterm Guide: Algebraic Structure, Ordered Ring, Monoid

• School: University of Illinois
• Department: Mathematics
• Course: MATH 417
• Professor: All

Document Summary

Second practice midterm (1) let a be a ring and end(a) the set of ring endomorphisms (i. e. , ring homomorphisms from a to itself). Assume that j is an ideal of a b and show that (a, b(cid:48)), (a(cid:48), b) j implies (a, b) j. (4) let i and j be two ideals in a ring a. I + j = {a + b a : a i, b j} is an ideal in a. (5) show that if an ordered ring a is bounded above and below then. A = {0}. (6) bonus: let s be a subset of the set x. Let a be the ring of real-valued functions on x, map(x, r) (with the usual addition and multiplica- tion). Let j be the subset of functions that vanish on s. show that.