Nyob rau hauv paub daws teeb meem algebra, ib qho semiring yog tus qauv algebraic zoo ib yam li lub nplhaib, tab sis tsis muaj qhov yuav tsum tau ua kom txhua lub ntsiab lus yuav tsum muaj qhov sib ntxiv ntxiv.
Puas yog cov lej ntuj ib nrab?
The semiring of natural tooj (N, +, ×) forms a commutative semiring.
Lub nplhaib nyob rau hauv txoj kev xav yog dab tsi?
Definition. Lub nplhaib yog a teeb R nruab nrog ob txoj haujlwm binary + (ntxiv) thiab ⋅ (multiplication) txaus siab rau cov hauv qab no peb pawg ntawm axioms, hu ua lub nplhaib axioms. R yog ib pab pawg abelian nyob rau hauv ntxiv, txhais tau tias: (a + b) + c=a + (b + c) rau tag nrho a, b, c hauv R (uas yog, + yog koom nrog).
Vim li cas lub nplhaib hu ua lub nplhaib?
Lub npe "ntiv nplhaib" yog muab los ntawm Hilbert lub sij hawm "Zahlring" (ntiv nplhaib tooj), qhia hauv nws Zahlbericht rau qee lub nplhaib ntawm cov lej lej.
Dab tsi yog pawg Monoid?
A monoid yog a teeb uas raug kaw hauv kev ua haujlwm binary koom nrog thiab muaj cov khoom ntiag tug xws li rau txhua tus,. Nco ntsoov tias tsis zoo li ib pab pawg, nws cov ntsiab lus yuav tsum tsis muaj inverses. Nws kuj tseem tuaj yeem xav tias yog ib pawg semigroup nrog cov cim cim. Ib qho monoid yuav tsum muaj tsawg kawg ib lub ntsiab lus.
