
beejganitiya siddhant

anaupchaarik roop seey ganitiya tark mein, ack beejganitiya siddhant ack aisaa siddhant haye joe mukt charr key saath shabdon key beach samikaranon key sandarbh mein poori tarah seey bataae gaye swayamsiddh kaa upayog kartaa haye. asamaantaon aur matrakon koo vishesh roop seey aswikar curr diyaa jaataa haye. samvedi tark pratham-crum tark kaa upasamuchchay haye jisamen kewal beejganitiya vaakya shamil hain.
yeh dhaarana beejganitiya sanrachana kii dhaarana key bahut karib haye, joe yakinan, sirf ack paryaay hoe sakata haye.
yeh kahana kii ack siddhant beejganitiya haye, yeh kahane kii tulanaa mein ack majboot sthiti haye kii yeh praathamik haye.
anaupchaarik vyakhya.
ack beejganitiya siddhant mein atirikt niyamon (swayamsiddh) key saath "aine"-airee karyatmak shabdon kaa sangrah hotaa haye.
udaaharan key liye, samoohon kaa siddhant ack beejganitiya siddhant haye kyonki isake teen karyatmak shabd hainh ack dwiaadhaari operation "a" × "b", ack shoonya operation 1 (tatasth tatva), aur ack ekaatmak operation "x" ′ "x" −1 kramshah sahakriyashilta, tatasthata aur vyutkram key niyamon key saath. anya udaharanon mein shamil hainh
yeh jyaamitiya siddhant key vipareet haye jisamen aanshik kaary (yaa dwiaadhaari sambandh) yaa astitvagat matra shamil hain-dekhein ee.jee. euclidean jyaamiti jahan binduon yaa rekhaaon kaa astitva abhinirdhaarit haye.
shreni-adharit model-saiddhaantik vyakhya.
ack beejganitiya siddhant t ack shreni haye jisaki vastuein praakritik sankhyaaen 0,1,2 hain.., aur joe, pratyek "aine" key liye, rupankanon kaa ack "aine"-tupal haih
yeh "aine" koo 1 kii "aine" pratiyon key cartasian utpaad key roop mein vyakhya karane kii anumati detaa haye.
udaaharan key liyeh aaie ack beejganitiya siddhant koo paribhaashit karein joe home ("aine", "aim") koo "aine" mukt charr "x" 1 key bahupadon key "aim"-tooples key roop mein letaa haye..., x" "n" purnank gunank key saath aur sanrachana key roop mein pratisthaapan key saath.  iss mamle mein "proji" "xi" key samaan haye. iss siddhant "tii" koo commutative rings kaa siddhant kahaa jaataa haye.
ack beejganitiya siddhant mein, kissy bhee rupankan "aine" "aim" koo hastakshar "aine" "" 1 key roop mein varnit kiya jaa sakata haye. inn baad key rupankan koo siddhant kaa "aine"-arrie "sanchaalan kahaa jaataa haye.
yadi "ee" seemit utpaadon key saath ack shreni haye, tou functors kii shreni kaa poorna upashreni alg (tii, ee) [tii, ee] una functors seey yukt haye joe seemit utpaadon koo sanrakshit karate hain, jise "tii-model" yaa tii-"algebra" kii shreni kahaa jaataa haye.
dhyaan dein kii operation 2 → 1 key mamle mein, upayukt beejganit "aeye" ack roopvaad koo paribhaashit karega.