This corresponds to the sum of transcript copies as 615,944 and 615,771 tpm (transcript per million).
For the 20-bp tag collections, the numbers of unique UniGene identifiers were slightly smaller: 5,793 and 5,125 for MRP1 and MRP2, respectively, which corresponds to the sum of transcript copies as 655,919 and 652,588 tpm.
By (3.10), the sum is a sum of copies of a random variable, say, such that (3.22).
Also, for a module (M), (oplus _{i=1}^{infty }M) stands for countably infinite direct sum of copies of (M).
Recall that a module (M) is called (Sigma )-injective if every direct sum of copies of (M) is injective.
In order that the socle of Y / X is a direct sum of copies of S ( a ), either X = Y (and Y / X = 0 ), or X = 0 (and Y / X = Y ), or X has to be indecomposable.
Since C is the projective module P ( a ), the right minimal right C -determined maps f : X → Y are the inclusions maps of submodules X of Y such that the socle of Y / X is a direct sum of copies of S ( a ).
So let us assume that i ≥ 2. A map f : X → Y is right P i -determined if and only if its kernel is a direct sum of copies of P i - 2. Since Ext 1 ( P i + 1, P i - 2 ) = D Hom ( P i, P i + 1 ) is a two-dimensional vector space, we see that we deal with short exact sequences of the form Open image in new window.
A projective polymodule will be called finitely generated if it is a submodule of a finite sum of copies of U (a, b ).
