2. Evaluate the Integral viling any qPPMpriare algebreic mettad or igohomerry identy

Let be as described in the proof of Theorem. Give a specific example of a positive element of .

[Type here] 18. Prove that only idempotent elements in an integral domain are and . [Type here]

For an element x of an ordered integral domain D, the absolute value | x | is defined by | x |={ xifx0xif0x Prove that | x |=| x | for all xD. Prove that | x |x| x | for all xD. Prove that | xy |=| x || y | for all x,yD. Prove that | x+y || x |+| y | for all x,yD. Prove that | | x || y | || xy | for all x,yD.