本书内容如下为例：

Abelian category

 An additive category C,
which satisfies the following conditions, for any
morphism f ∈ HomC(X,Y):
(i.) f has a kernel (a morphism i ∈ HomC
(X,X) such that fi = 0) and a co-kernel (a
morphismp ∈ HomC(Y,Y) such that pf = 0);
(ii.) f may be factored as the composition of
an epic (onto morphism) followed by a monic
(one-to-one morphism) and this factorization is
unique up to equivalent choices for these morphisms;
(iii.) if f is a monic, then it is a kernel; if f
is an epic, then it is a co-kernel.
See additive category.
Abel’s summation identity If a(n) is an
arithmetical function (a real or complex valued
function defined on the natural numbers), define
A(x) =
0 ifx < 1 ,
n≤x
a(n) if x ≥ 1 .
If the function f is continuously differentiable
on the interval [w, x], then
 w<n≤x
a(n)f(n) = A(x)f(x)
−A(w)f(w)
−  x
w
A(t)f(t) dt .
abscissa of absolute convergence For the
Dirichlet series ∞
n=1
f(n)
ns , the real number σa, if it
exists, such that the series converges absolutely
for all complex numberss = x+iy withx > σa
but not for any s so that x < σa. If the series
converges absolutely for all s, then σa = −∞ and if the series fails to converge absolutely for
any s, then σa = ∞. The set {x +iy : x > σa} is called the half plane of absolute convergence
for the series. See also abscissa of convergence.