(Hungerford exercise 31, page 143)
Let R be a commutative ring without identity and let
Show that is an ideal containing a and that every ideal containing a also contains A. (A is called the prinicipal ideal generated by a)
(Hungerford exercise 31, page 143)
Let R be a commutative ring without identity and let
Show that is an ideal containing a and that every ideal containing a also contains A. (A is called the prinicipal ideal generated by a)
For the first one: take
For the second one: In an ideal , multiplication by elements in and addition by elements in produces elements in . The result should now be obvious (though you should prove it more rigorously, shouldn't be more than a few lines).