The endlich Baer splitting property

On the Universal Splitting Property

We prove that if an incomplete computably enumerable set has the the universal splitting property then it is low 2. This solves a question from Ambos-Spies and Fejer 1] and Downey and Stob 7]. Some technical improvements are discussed.

A Splitting Property of Maximal Antichains

In every dense poset P every maximal antichain S may be partitioned into disjoint subsets S1 and S2 , such that the union of the upset of S1 with the downset of S2 yields the entire poset: U(S1) [ D(S2) = P . To nd a similar splitting of maximal antichains in posets is NP{hard in general.

Scheduling Jobs on Several Machines with the Job Splitting Property

This scheduling model is derived from the real problem of scheduling looms in a textile industry. Jobs may be independently split over several specified machines and preemption is allowed. Deadlines are specified for each job and jobs are assumed to be available. It is shown that minimizing maximum weighted tardiness can be done in polynomial time. The case of uniform machines (as in the consid...

Locally Compact Baer Rings

Locally direct sums [W, Definition 3.15] appeared naturally in classification results for topological rings (see, e.g.,[K2], [S1], [S2], [S3], [U1]). We give here a result (Theorem 3) for locally compact Baer rings by using of locally direct sums. 1. Conventions and definitions All topological rings are assumed associative and Hausdorff. The subring generated by a subset A of a ring R is denote...

Extensions of Baer and quasi-Baer modules