‎We call a ring $R$ right generalized semiperfect if every simple right $R$-module is an epimorphic image of a flat right $R$-module with small kernel‎, ‎that is‎, ‎every simple right $R$-module has a flat $B$-cover‎. ‎We give some properties of such rings along with examples‎. ‎We introduce flat strong covers as flat covers which are also flat $B$-covers and give characterizations of $A$-perfe...

‎we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel‎, ‎that is‎, ‎every simple right $r$-module has a flat $b$-cover‎. ‎we give some properties of such rings along with examples‎. ‎we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...

In this work, we investigate in the problem of perfect matchings with prescribed matchings in the n-dimensional hypercube network Qn. We obtain the following contributions: For any arbitrary matching with at most n − 1 edges, it can be extended to a perfect matching of Qn for n ≥ 1. Furthermore, for any arbitrary non-forbidden matching with n edges, it also can be extended to a perfect matching...

In this lecture, the focus is on general perfect matching problem where the goal is to prove that it can be solved in polynomial time by linear programming. Based on the LP formulation for bipartite matching studied in Lecture 10, we add some valid inequalities to establish a new formulation. Then we prove that for general perfect matching, all vertex solutions of the linear program are integra...

Consider independent fair coin-flips at each site of the lattice Z d. A translation-equivariant matching rule is a perfect matching of heads to tails that commutes with translations of Z d and is given by a deterministic function of the coin-flips. Let Z Φ be the distance from the origin to its partner, under the translation-equivariant matching rule Φ. Holroyd and Peres [9] asked what is the o...

The perfect matching problem is known to be in ¶, in randomized NC, and it is hard for NL. Whether the perfect matching problem is in NC is one of the most prominent open questions in complexity theory regarding parallel computations. Grigoriev and Karpinski [GK87] studied the perfect matching problem for bipartite graphs with polynomially bounded permanent. They showed that for such bipartite ...