Fraleigh (A First Course in Abstract Algebra) defines principal ideals in section 27 on page 250. His definition is as follows:

================================================== =============================================

"27.21 Definition

If R is a commutative ring with unity and , the ideal of all multiples of a is the principal ideal generated by a and is denoted <a>.

An ideal N of R is a principal ideal if N = <a> for some

================================================== ===============================================

Consider ...........................(1)

If we take r = a in (1) then we have

If we take r = a and the we have using (1) again that

Continuing this, then we have , .... all belonging to N along with the other elements where

Is the above analysis correct regarding the nature of principal ideals?

Would really appreciate this issue being clarified.

Peter