Sentence examples for graded coprime from inspiring English sources

Clearly, two distinct graded maximal submodules of a graded module are graded coprime.

Since N and K are graded coprime submodules in a graded finitely generated module M, we have R M = M = N + K = I M + J M = ( I + J ) M. Open image in new window.

Let R be a G-graded commutative ring with identity, and let M be a G-graded module over R. Two graded submodules N and K of graded module M are called graded coprime whenever N + K = M.

Let R be a graded ring and M be a graded multiplication module over R. Let N and K be graded coprime submodules of M.

For example, we show that if M is a graded finitely generated module, then two graded submodules N and K of M are graded coprime if and only if grad M (N) and grad M (K) are graded coprime.

Let R be a graded ring and M be a graded module over R; two graded submodules N and K of M are called graded coprime whenever N + K = M.

(2) Normal grading > reverse grading.

In this paper, rate distortion performance of nested sampling and coprime sampling is studied.

Figure 4 Rate distortion performance-coprime sampling.

Assuming M and N are the coprime pair and T s is the sampling rate.

Because x and y are coprime, so that x and N are coprime, it follows (from some theorem of the theory of cyclical groups that I forgot a long time ago) that this method generates the entire group, i.e., all integers 0, 1, …, N (and N is the last such generated, i.e., is adjacent to 0 on the clockwise side).