جبر حلقات - اسئلة بحاجة الى الحل

السلام عليكم ورحمة الله وبركاته

[

SIZE=5]

Let f:R→R ́ be a ring homo. Onto prove that 1
ٌٌ I is a prime ideal of R with ker⁡〖f 〗⊆I ⇒f(I) is a prime ideal of R' ٌ ́.
J is a prime ideal of R ́⇒ f^(-1) (J) is a prime ideal of R .

Let R be com. Ring with unity if every ideal of R is a prime ideal prove that
R is a field .

[/SIZE]