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Let S be a finite nonabelian simple group, and let H be a subgroup of S . In this work, the dominion (in the sense of Isbell) of H in S in Var(S) is determined, generalizing an example of B.H. Neumann. A necessary and sufficient condition for H to be epimorphically embedded in S is obtained. These results are then extended to a variety generated by a family of finite nonabelian simple groups. S...

We continue the studies of the second author on regulated uniformly k-limited and regulated k-limited ET0L systems. We focus on the permitting and forbidding random context regulation. Especially, we establish some results on (regulated) propagating (uniformly) k-limited ET0L systems which were not solved in 2, 18, 21, 22]. Moreover, relations to recurrent programmed languages introduced by von...

This article describes the addition to the von Neumann cellular automaton of the Tom Thumb Algorithm, a mechanism developed for the self-replication of multi-processor systems. Except for the cell construction process, every functionality of the original CA has been preserved in our new system. Moreover, the Tom Thumb Algorithm now allows the replication of any structure within the von Neumann ...

A longstanding open problem in the theory of von Neumann regular rings is the question of whether every directly finite simple regular ring must be unit-regular. Recent work on this problem has been done by P. Menal, K.C . O'Meara, and the authors. To clarify some aspects of these new developments, we introduce and study the notion of almost isomorphism between finitely generated projective mod...

Die Aussagekraft betrieblicher Daten kann durch die Nutzung von Unternehmensvergleichen wesentlich erhöht werden. An einem Beispiel von Gesundheitsdaten beim Milchrind werden die informationstechnologischen Voraussetzungen zur Umsetzung eines entsprechenden Konzeptes erläutert. Schwerpunkte bilden dabei die Bereitstellung, die Vergleichbarkeit, die Übertragung und die Präsentation der Daten.

We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L2rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ, or are weakly rigid. As a consequence we obtain that ...

It is shown that for any commutative unital ring R the category HopfR of R–Hopf algebras is locally presentable and a coreflective subcategory of the category BialgR of R–bialgebras, admitting cofree Hopf algebras over arbitrary R–algebras. The proofs are based on an explicit analysis of the construction of colimits of Hopf algebras, which generalizes an observation of Takeuchi. Essentially be ...

It is known that every dimension group with order-unit of size at most א1 is isomorphic to K0(R) for some locally matricial ring R (in particular, R is von Neumann regular); similarly, every conical refinement monoid with order-unit of size at most א1 is the image of a V-measure in Dobbertin’s sense, the corresponding problems for larger cardinalities being open. We settle these problems here, ...