
wederburn-artin pramey

beejganit mein, wederburn-artin pramey ardh-saral valay aur ardh-saral algebra key liye ack vargeekaran pramey haye. pramey mein kahaa gayaa haye kii ack (artinian) ardh-saral valay "r" vibhajan valayon parr parimit roop seey kaee-dwara-matricks valayon key utpaad key liye samroop haye, kuchh purnankon key liye, joe donon soochkaank key kramparivartan taka vishisht roop seey nirdhaarit kiye jaate hain. vishesh roop seey, koee bhee saral baaen yaa daaen kalaatmak valay ack vibhajan valay "d" parr "n"-dwara-"n" matricks valay key liye samroop haye, jahan "n" aur "d" donon vishisht roop seey nirdhaarit hotey hain.
pramey.
ack (kalaatmak) ardh-saral angoothi honey dein. phir wederburn-artin pramey bataati haye kii kuchh purnankon key liye, joe soochkaank key kramparivartan taka vishisht roop seey nirdhaarit kiye jaate hain, vibhajan valay parr parimit roop seey kaee-dwara-matricks ring sootra _ 1 key utpaad key liye samroop haye. 
ack kshetra parr algebra key liye wederburn-artin pramey kaa ack sanskaran bhee haye. yadi ack parimit-ayami ardh-saral-beejganit haye, tou uparokt kathan mein pratyek ack seemit-ayami vibhajan beejganit haye. pratyek kaa kendra honah aavashyak naheen haye; yeh ack seemit vistaar hoe sakata haye.
dhyaan dein kii yadi ack vibhajan valay "ee" parr ack parimit-ayami saral beejganit haye, tou "dee" koo "ee" mein nihit karane kii aavashyakta naheen haye. udaaharan key liye, jatil sankhyaon parr matricks ring vaastavik sankhyaon parr parimit-ayami saral algebra hain.
pramaan.
wederburn-artin pramey key vibhinn pramaan hain. ack samanya aadhunik nimnalikhit drishtikon apanaata haye. 
maan leejiye kii ring sootra _ 2 ardh-saral haye. phir sahee sootra _ 2-module sootra _ 4 saral module key ack seemit pratyaksh yog key liye samroop haye (joe sootra _ 2 key nyuntam sahee aadarshon key samaan hain). iss pratyaksh raashi koo iss prakaar likhein
jahan sootra _ 7 parasparik roop seey gair-samroop saral sootra _ 2-module hain, vaha gunan sootra _ 9 key saath dikhaai detaa haye. yeh endomorphism rings kaa ack samroopata detaa haye.
aur humm matricks key ack ring key saath sootra _ 11 kii pehchaan curr sakate hain
jahan sootra _ 7 kaa endomorphism ring sootra _ 13, shoor key lemma dwara ack vibhajan ring haye, kyonki sootra _ 7 saral haye. sootra _ 16 key baad seey humm nishkarsh nikaalate hain
yahaan hamane sahee module kaa upayog kiya kyonki sootra _ 16; yadi humm baaen module kaa upayog karate hain tou sootra _ 2 sootra _ 20 key vipareet beejganit key liye samroop hoga, lekin pramaan abhee bhee gujarta rahega. iss pramaan koo ack badey sandarbh mein dekhane key liye, ack module kaa apghatan dekhein. ack mahatvapurna vishesh mamle key pramaan key liye, saral artinian angoothi dekhein.
parinam.
choonki ack kshetra parr ack parimit-ayami beejganit artinian haye, wederburn-artin pramey kaa tatparya haye kii ack kshetra parr pratyek seemit-ayami saral beejganit sootra _ 21 parr kuchh seemit-ayami vibhajan beejganit parr ack "aine"-baaee-"aine" matricks ring key liye samroop haye, jahaan "aine" aur "dee" donon vishisht roop seey nirdhaarit kiye jaate hain. yeh joseph wederburn dwara dikhaaya gayaa thaa. emil artin ney baad mein iss parinam koo saral baaen yaa daaen artinian ring key mamle mein saamaanyikrit kiya. 
choonki beejganitiya roop seey bund kshetra parr ekmatra parimit-ayami vibhajan beejganit kshetra hii haye, isaliye iss mamle mein wederburn-artin pramey key majboot parinam hain. maan leejiye kii ack ardh-saral valay haye joe ack beejganitiya roop seey bund kshetra sootra _ 21 parr ack parimit-ayami beejganit haye. phir ack seemit utpaad sootra _ 23 haye jahan sootra _ 24 sakaratmak purnank hain aur sootra _ 25 sootra _ 21 parr sootra _ 26 metrices kaa beejganit haye. 
isake alawa, wederburn-artin pramey ack kshetra sootra _ 21 parr parimit-ayami kendriya saral algebra koo vargeekrit karane kii samasya koo cumm curr detaa haye, joe kii sootra _ 21 parr seemit-ayami kendriya vibhajan algebra koo vargeekrit karane kii samasya haih arthaat, sootra _ 21 parr vibhajan algebra jiska kendra sootra _ 21 haye. iska tatparya haye kii sootra _ 21 parr koee bhee seemit-ayami kendriya saral beejganit ack matricks beejganit sootra _ 33 key liye samroop haye.
jahan sootra _ 34 sootra _ 21 parr ack parimit-ayami kendriya vibhajan beejganit haye.

