MAT 305 Fall'07 Test 1
SHOW ALL YOUR WORK TO GET PARTIAL CREDIT.
1. Find the order of each element in the indicated group: (a) 6 in Z15 (b) ( 2 7 3 )( 1 2 4 ) in S8 , (c) 11 in U(14) and 2. Let G = <a> be a cyclic group with order |G| = 15 (a) List
MAT 305 Review for Test 2 1. Important definitions: Rings, integral domains, fields, units, zero divisors, characteristic of a ring, ring homomorphism, ring isomorphism, ideals, prime ideals, maximal ideals, principal ideals, quotient ring, ring of p
MAT 305 Test 2
I. List all the units and in each case find its multiplicative inverse in : (a) Z8 , (b) Z [i] , (c) Z7[x] , (d) Q( 2)
II. Find all the zero divisors ( if any ) in : (a) Z7[x] , (b) Z6[x] , (c) Z2 x Z3 , (d) Z [i]
MAT 305 Review for Test 1 1. Important Definitions: groups, subgroups, subroup lattice, order of an element, Abelian groups, order of a group, Euler phi-function, cyclic groups, generators of cyclic groups, permutations, groups of permutations, odd e