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question 1the national association of college and university business officers researched the change in university and
seven women and nine men are on the faculty in the mathematics department at a schoolahow many ways are there to select
a certain city has experienced a relatively rapid increase in traffic congestion in recent times the mayor has decided
prove that z5x2 x 1 is a field how many elements are there in this field can you also represent it as z5xx2-a where a
show that n is contained in p for each prime ideal p of a commutative ring rwhere n is the set of all nilpotent
let show that the map the residue of a b modulo 2 is a ring homomorphism with prove that hence or otherwise give a
let prove that the map given by where is the residue of a modulo n is a ring homomorphism find the kernel and image
note z is integer numbersc is set containmenthere is the problemlet i be an ideal in a ring rdefine r i r in r
1 let r be a ring prove that if x y e r such that xy is right quasi-regular then yx is also right quasi-regular2 let m
i show that if d is an integral domain then dx is never a fieldii is the assumption d is an integral domain needed here
1ler r be a ring and prove using axioms for a ring the followingthe identity element of r s uniquethat -r is the
let uxt describe the temperature of a thin metal ring with circumference 2pi for convenience lets orient the ring so
let p be a prime and let g be an abelian group of order a power of pprove that the nilradical of the group ring g is
let f k be two fields f is a subset of k and suppose fx gx amp1028 fx are relatively prime in fx prove that they are
if fx x5 2x3 x2 2x 3 gx x4 x3 4x2 3x 3 then find greatest common divisor of fx and gx over the field of
let r be an integral domain m a maximal ideal let sr-maprove that s-1r is a local ringbsuppose rz m5 describe
modern algebraring theory viiithe field of quotients of an integral domainprove the distributive law in f the field of
let r be a ring with the property that every element is either nilpotent or invertible if a b c are in r with a and b
let i be a non-empty index set with a partial orderlt assume that i is a directed set that is that for any pair ij in i
let i be a non-empty index set with a partial order lt and ai be a group for all i in i suppose that for every pair of
let phir-gts be a homomorphism of commutative ringsa prove that if p is a prime ideal of s then either phi-1pr or
let s be a subset of a set x let r be the ring of real-valued functions on x and let i be the set of real-valued
i am given the set of infinite-by-infinite matrices with real entries that have only finitely many nonzero entries also
1 if e f are fields and f is a subring of e show each q in autef permutes the roots in e of each nonzero px in fx hint