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 $\varphi$.
Beyond zero tolerance : discrimination in military culture
Chapter 1 Introduction: Rethinking Military Culture Part 2 Constructing Military Culture Chapter 3 Discrimination and Military Cohesion: An Organizational Perspective Chapter 4 Military Folk Culture Chapter 5 Dressed to Kill? The Paradox of Women in Military Uniforms Chapter 6 A Tangled Webb the Navy Can't Afford Chapter 7 Women at the U.S. Army War College Part 8 The Military, Society, and Policy Chapter 9 Reflections of Society: The Intersection of Race and Gender in the U.S. Army in World War II Chapter 10 Intersectionality: A Necessary Consideration for Women of Color in the Military? Chapter 11 In War and Peace: Incidence and Implications of Rape by Military Personnel Chapter 12 Persistence of Sexual Harassment: The Impact of Military Culture on Policy Implementation Chapter 13 A Culture of Silence: Consequences of Don't Ask, Don't Tell, Don't Pursue Chapter 14 Gender and Sexual Orientation Diversity in Modern Military Forces: Cross-National Patterns Chapter 15 Military Culture and Military Families