I'm working on a practice exam for my major field exam, and I have not taken abstract algebra yet, so these problems are giving me trouble. I only need help with one of them though:
Let R be a ring with the binary operations + and * and let I be an ideal of R. Which of the following is/are true?
I. and ,
II. and ,
III. and ,
IV. and ,
V. and ,
I know that II and V are true, and I know that III is false, but I'm not entirely certain about IV (though I suspect it is true) and V.