线性空间
(V)为非空集合，(K)为数域，(V)为(K)上的线性空间
((i)forall alpha,eta,gamma in V,alpha+(eta+gamma)=(alpha+eta)+gamma)
((ii)alpha+eta=eta+alpha)
((iii)exists0in V,forall alpha in V,alpha+0=alpha)
((iv)forall alpha in V,exists eta ,alpha+eta=0)
((v)exists 1,1cdot alpha=alpha)
((vi)forall k,l in K,alpha in V,(kl)alpha=k(lalpha))
((vii)forall k,l in K,alphain V，(k+l)alpha=kalpha+lalpha)
$(viii)forall kin K,alpha ,eta in V,k(alpha+eta)=kalpha+keta $
二次型
一元多项式环
(f(x),g(x)in K[X],f(x))