Here you are assuming that R contains unity which kind of the defeats the purpose. Since (u) = (ru + nu ; r belongs to R and n belongs to Z). This is the definition of principal ideal. (u) = ru only when R is integral domain and contains unity. Since it is possible that u != ru for any element, that's why the definition of principal ideal contains ru + nu, so ru + nu = u for some r and n. By definition , Principal ideal generated by a is the smallest ideal containing a.
Sir thanku ap bhut accha padhte ho
Thanks n welcome dear
Here you are assuming that R contains unity which kind of the defeats the purpose. Since (u) = (ru + nu ; r belongs to R and n belongs to Z). This is the definition of principal ideal. (u) = ru only when R is integral domain and contains unity. Since it is possible that u != ru for any element, that's why the definition of principal ideal contains ru + nu, so ru + nu = u for some r and n. By definition , Principal ideal generated by a is the smallest ideal containing a.
Ring of gaussian integers is an euclidean domain par video bana do
Ok dear
@@MathematicsAnalysis sir principal idea domains par bhi
Sir aap lpp karao numerical nhi please aur sir real me b.sc Ka ek important serise banaye sabse jayada real me problam Hoti hai
Playlist dekhlo sare question available h
@@MathematicsAnalysis ok.limit me kuch proof aata hai problam Ka co nhi Katayama aur complex me limit continuity and diffrencibility nhi karaya