Linear equations over finite abelian groups
One of the oldest problems in algebra is the solution of a system of linear equations over certain domains. The Gaussian elimination algorithm provides an effective solution over fields. The Smith normal form algorithm yields a method over the integers. Here we consider another variation of this theme. Let A be a finite (additive) abelian group, let αi,j ∈ End(A) for 1 ≤ i ≤ n and 1 ≤ j ≤ m and let b1, . . . , bm ∈ A. Then we want to determine the set S of all (x1, . . . , xn) ∈ A n with
Solving linear equations over finitely generated abelian groups
We discuss various methods and their effectiveness for solving linear equations over finitely generated abelian groups. More precisely, if $\varphi\colon G\to H$ is a homomorphism of finitely generated abelian groups and $b\in H$, we discuss various algorithms for checking whether $b\in \im\varphi$ holds and if so, for computing a pre-image of $b$ in $G$ together with the kernel of $\varphi$.
China's rise in Asia : promises and perils
Chapter 1 Salient Determinants of China's Recent Approach to Asia and its Implications for the United States Chapter 2 Recent Chinese Domestic and Foreign Policies and Priorities Chapter 3 China's Relations with the United States Chapter 4 China's Relations with Russia Chapter 5 Relations with Japan Chapter 6 Relations with the Korean Peninsula Chapter 7 China-Southeast Asia Relations Chapter 8 Relations with Taiwan Chapter 9 Relations with South Asia Chapter 10 Relations with Central Asia Chapter 11 Conclusion: China's Peaceful Approach to Asia and its Implications for the United States