
bee. key. beejganit

ganit mein, bci aur bck algebra saarvbhaumik beejganit mein beejganitiya sanrachanaaen hain, jinhen y dwara pesh kiya gayaa thaa. imai, key. iski aur aiss. 1966 mein taanaa, joe bee. see. aaee. aur bee. key. key. logics key roop mein jaane jaane vaale nihitarth seey judey prastavatmak cullon key tukadon kaa varnan kartaa haye.
paribhasha.
bci beejganit.
ack beejganit (saarvbhaumik beejganit key arth mein) sootra _ 2 key prakaar key sootra _ 1 koo "bci-beejganit" kahaa jaataa haye yadi, kissy sootra _ 3 key liye, yeh nimnalikhit sharton koo santusht kartaa haye. (anaupchaarik roop seey, humm sootra 4 koo "satya" key roop mein aur sootra 5 koo "sootra 6 kaa tatparya sootra 7" key roop mein padh sakate hain.)
bee. key. beejganit.
ack bci-beejganit sootra _ 13 koo "bc-beejganit" kahaa jaataa haye yadi yeh
nimnalikhit sharton koo puuraa kartaa haih
ack aanshik crum koo taba "x" ≤ "y" key roop mein paribhaashit kiya jaa sakata haye yadi x * y = 0 hoe.
bee. key.-beejganit koo "parivartaniya" kahaa jaataa haye yadi yeh santusht kartaa haih
ack commutative bck-beejganit mein "x" * ("x" * "y") = "x" Â "y" aanshik crum ≤ key tahat "x" aur "y" kii sabse badee nichali seema haye.
ack bee. key. beejganit koo taba seemit kahaa jaataa haye jaba iska sabse badaa tatva hotaa haye, jise aamtaur parr 1 seey darshaaya jaataa haye. ack seemit commutative bee. key.-beejganit mein dou tatvon kii sabse cumm oopari seema "x" Â "y" = 1 * ((1 * "x") Â (1 * "y") koo santusht karati haye; joe ise ack vitaran jaali banaata haye.
udaaharan.
pratyek abelian samooh ack bci-beejganit haye, jisamen * koo samooh ghataav key roop mein paribhaashit kiya gayaa haye aur 0 koo samooh pehchaan key roop mein paribhaashit kiya gayaa haye.
ack samooh key upasamuchchay ack bck-beejganit banaate hain, jahan a * b antar a\b haye (a mein tatva lekin b mein naheen), aur 0 khaali samooh haye.
booliyan beejganit ack bee. key. beejganit haye yadi "aeye" * bee "koo" aeye "bee" ("aeye" kaa arth "bee" naheen haye) key roop mein paribhaashit kiya gayaa haye.
bounded commutative bee. key.-algebra thheek aim. vee.-algebra hain.