  We prove the following results (1) (2) (3) on relations between $n$-links and
their components. (1) Let L=(L_1, L_2) be a (4k+1)-link (4k+1\geq 5). Then we
have Arf L=Arf L_1+Arf L_2. (2) Let L=(L_1, L_2) be a (4k+3)-link (4k+3\geq3).
Then we have \sigma L=\sigma L_1+\sigma L_2. (3) Let n\geq1. Then there is a
nonribbon n-link L=(L_1, L_2) such that L_i is a trivial knot.
  We prove the following results (4) (5) (6) (7) on band-sums of n-links. (4)
Let L=(L_1, L_2) be a (4k+1)-link (4k+1\geq 5). Let K be a band-sum of L. Then
we have Arf K=Arf L_1+Arf L_2. (5) Let L=(L_1, L_2) be a (4k+3)-link
(4k+3\geq3). Let K be a band-sum of L. Then we have \sigma K=\sigma L_1+ \sigma
L_2.
  The above (4)(5) imply the following (6). (6) Let 2m+1\geq3. There is a set
of three (2m+1)-knots K_0, K_1, K_2 with the following property: K_0 is not any
band-sum of any n-link L=(L_1, L_2) such that L_i is equivalent to K_i (i=1,2).
(7) Let n\geq1. Then there is an n-link L=(L_1, L_2) such that L_i is a trivial
knot (i=1,2) and that a band-sum of $L$ is a nonribbon knot.
  We prove a 1-dimensional version of (1). (8) Let L=(L_1, L_2) be a proper
1-link. Then Arf L =Arf L_1+ Arf L_2+{1/2}\{\beta^*(L)$+mod4 $\{{1/2}lk (L)\}\}
  =Arf L_1+Arf L_2+mod2 \{\lambda (L)\}, where \beta^*(L) is the
Saito-Sato-Levine invariant and \lambda(L) is the Kirk-Livingston invariant.
