Now [[omega].sub.0](h-Fix(f/p)) is just the direct sum
[[direct sum].sub.[gamma]] Z[[gamma]], of copies of Z indexed by the components [gamma] of h-Fix(f/p), and we can decompose h-L(f/p) as
Part 1 of Definition 2.1 is equivalent to Bejancu's original definition , the distributions D, [D.sup.[perpendicular to]] of  being the terms of the direct sum
If A is a g-Drazin invertible operator in a Banach space X, then X = R([A.sup.D]A) [direct sum] N([A.sup.D] A), A = [A.sub.1] [direct sum] [A.sub.2], where [A.sub.1] is closed and invertible, [A.sub.2] is bounded and quasinilpotent with respect to this direct sum
A submodule B [subset or equal to] M is a basic submodule of M, if B is h-pure in M, B = [direct sum] [B.sub.i], where each [B.sub.i] is the direct sum
of uniserial modules of length i and M/B is h-divisible.
Then [M.sub.1] [direct sum] [M.sub.2] is a matroid - the direct sum
of [M.sub.1] and [M.sub.2].
The Direct sum
[Ha.sub.i] [direct sum] [Ha.sub.j]: i [not equal to] j forms an AG-subgroupoid.
They said a direct sum
of over ` 55,398 crore had been invested in Games- related projects and the rest was in the form of indirect activities.
It is well known (see e.g., Fuchs 1970) that minimal pure-injective group containing a given group G as a pure-subgroup is isomorphic to the direct sum
of the divisible hull of the Ulm subgroup G1 of G and the Z-adic completion of G.
of Dundee, Scotland) gently introduce the factorization theory of abelian groups, which deals with decomposing an abelian group into a direct sum
of its subsets.
where [direct sum] denotes the direct sum
. More precisely, if C [member of] S [intersection] A then [C.sup.*] = C and [C.sup.*] = -C.
Britain is the second largest net contributor to the EU budget, after only Germany, paying a direct sum
of pounds 15bn per year for membership of the EU.
The operation [direct sum]: the direct sum
of functions in the algebra of functions is similar to logic multiplication of the corresponding binary vectors components (operation AND) in the structural approach, i.e.