MAYDON

MAYDON dar algebra, majmuest, ki amalhoi arifmetikii jam, zarb, tarh va taqsimro dar bar megirad. Agar summai elementhoi a, bo a + va zarbi onho bo a ishorat karda shavad, ijro shudani aksnomahoi zayl shart ast:

1) a + <=> -j- a, ab = a\ 2\ (a + + ) + s ■ v + (6 + s), (ao) • s =

A (6s); 3) a(6 + s) = ab+as; 4) element 0 (sifr) mavjud ast, ki baroi on barobarii a + 0 = a va elementi az 0 farqkunandai 1 mavjud ast, ki baroi on barobarii a • 1 = *» a joy dorad; 5) muodilai a + kh = m 0 hal dorad, muodilai akh = 1 bo-shad, hangomi 0 budan hal dorad.

Dar hama guna Maydon muodilai a + + kh – halli yagona doshta, in hal bo kh — — a ishorat karda meshanad; dar holatp a^=0 budan, muodilai akh = niz ba halli yagona sohib ast va on bo kh = a-16 ishorat karda meshavad.

Misolhoi Maydon:

Har — majmui hamai adadhoi rasionali.

2) YA — majmui hamai adadhoi haqiqi.

3) G — majmui adadhoi kompleksi.

4) Majmui hamai funksiyahoi rasionalii yak yo bisyor tagyiryobanda, mas., bo koeffisientkhoi haqiqi.

5) Majmui hamai adadhoi namudi a 4- 6U5G” ki dar on a va 6 adadhoi rasionaliand va g.

Agar amalhoi jam va zarb dar majmui iborat aa adadkhoi 0, i, 2 (adadkhoe, ki badi taksim ba adadi 3          boqi memonand) bo tarzi dar tablisa tasviryofta muayyan karda shavand, aksiomahoi dar bolo nombarshuda ijro meshavand.

Dar in Maydon barobarii a + a + a = = 0 joy khohad dosht. Maydon dar nazariyai adadho va digar sohakhoi matematika istifoda meshavad.

Ad.: Kurosh A. G., Kurs visshey algebri, 11 izd., *M., 1075.