جبر حلقات - اسئلة بحاجة الى الحل

[عبدالرحمن ال حرفش]

السلام عليكم ورحمة الله وبركاته

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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 .

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