Minus partial order in regular modules

Minus Partial Order in Rickart Rings

The minus partial order is already known for complex matrices and bounded linear operators on Hilbert spaces. We extend this notion to Rickart rings, and thus we generalize some well-known results.

Partial second-order subdifferentials of -prox-regular functions

Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2  functions. The class of prox-regular functions covers all convex functions, lower C2  functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...

Minus domination in regular graphs

A three-valued function f defined on the vertices of a graph G = (V,E), f : V , ( 1 , 0 , 1), is a minus dominating function if the sum of its function values over any closed neighborhood is at least one. That is, for every v E V, f(N[v])>~ 1, where N[v] consists of v and every vertex adjacent to v. The weight of a minus dominating function is f ( V ) = ~ f (v) , over all vertices v E V. The mi...

Ela Decomposition of a Ring Induced by minus Partial Order

The minus partial order linear algebraic methods have proven to be useful in the study of complex matrices. This paper extends study of minus partial orders to general rings. It is shown that the condition a < b, where < is the minus partial order, defines two triples of orthogonal idempotents, and thus, a decomposition of a ring into a direct sum of abelian groups. Hence, several well-known re...

Decomposition of a ring induced by minus partial order