
aparivartaniya aadarsh

ganit mein, ack commutative ring kaa ack uchit aadarsh aparivartaniya kahaa jaataa haye yadi ise dou sakhti seey badey aadarshon key pratichhedan key roop mein naheen likhaa jaa sakata haye. 
guna.
ack abhinn kshetra kaa ack tatva taba abhaajya hotaa haye jaba usake dwara utpann aadarsh gair-shoonya abhaajya aadarsh hoe. yeh irreducible ideals key liye sach naheen haye; ack irreducible ideal ack aise tatva dwara utpann kiya jaa sakata haye joe ack irreducible tatva naheen haye, jaisa kii aadarsh sootra _ 13 key liye sootra _ 9 mein haye kyonki yeh dou sakhti seey badey ideals kaa pratichhedan naheen haye.
ack ring "r" kaa ack aadarsh "i" kewal tabhi irreducible hoe sakata haye jaba beejganitiya sett jise yeh paribhaashit kartaa haye vaha zariski topology key liye irreducible (yaani, koee bhee khula subset ghanaa haye) haye, yaa samkaksh roop seey yadi "i" vaale prime ideals seey yukt speck "r" kaa bund sthaan varnakramiya topology key liye irreducible haye. parivartit naheen hotaa haye; udaaharan key liye pahale aur dusare crum key lupt honey vaale shabdon key saath dou charr mein bahupadon kaa aadarsh irreducible naheen haye.
yadi k ack beejganitiya roop seey bund kshetra haye, tou k parr ack bahupad valay key ack irreducible ideal key mool kaa chayan karna thheek usee tarah haye jaise kii affine sthaan mein isake nullstell kii affine vividhata kaa ack embedding chunana.