We treat centralizer near-rings over ring modules in general, with particular emphasis on the case of free modules. Questions like the following are answered. When is the near-ring a nonring? When is the near-ring simple? What are its maximal and minimal left ideals? What is its subgroup structure? What is the radical? The cases where the ring concerned is a PID or a field are treated in some detail.

The main result of this paper shows that the existence of commuting normal extension (c.n.e.) for an arbitrary family of commuting subnormal operators can be determined by considering appropriate families of multivariable weighted shifts. In proving this some known criteria for c.n.e. are generalized. It is also shown that a family of jointly quasi-normal operators has c.n.e.

On compact oriented differentiable manifolds, we define a well behaved Riemann type integral which coincides with the Lebesgue integral on nonnegative functions, and such that the exterior derivative of a differentiable (not necessarily continuously) exterior form is always integrable and the Stokes formula holds.

In this paper results from Fluctuation Theory are used to analyse the imbedded Markov chains of two single server bulk-queueing systems, (i)with Poisson arrivals and arbitrary service time distribution and (ii) with arbitrary inter-arrival time distribution and negative exponential service time. The discrete time transition probailities and the equilibrium behaviour of the queue lengths of the systems have been obtained along with distributions concerning the busy periods. From the general results several special cases have been derived.

This paper is concerned with a new notion of coherency for monoids. A monoid S is right coherent if the first order theory of right S-sets is coherent; this is equivalent to the property that every finitely generated S-subset of every finitely presented right S-set is finitely presented. If every finitely generated right ideal of S is finitely presented we say that S is weakly right coherent. As for the corresponding situation for modules over a ring, we show that our notion of coherency is related to products of flat left S-sets, although there are some marked differences in behaviour from the case for rings. Further, we relate our work to ultraproducts of flat left S-sets and so to the question of axiomatisability of certain classes of left S-sets.

We show that a monoid S is weakly right coherent if and only if the right annihilator congruence of every element is finitely generated and the intersection of any two finitely generated right ideals is finitely generated. A similar result describes right coherent monoids. We use these descriptions to recognise several classes of (weakly) right coherent monoids. In particular we show that any free monoid is weakly right (and left) coherent and any free commutative monoid is right (and left) coherent.

We investigate the asymptotical behaviour of the transition probabilities of the simple random walk on the 2-comb. In particular, we obtain space-time uniform asymptotical estimates which show the lack of symmetry of this walk better than local limit estimates. Our results also point out the impossibility of getting sub-Gaussian estimates involving the spectral and walk dimensions of the graph.

Let St = exp{−tH}, Tt = exp{−tK}, be C0-semigroups on a Banach space . For appropriate f one can define subordinate semigroups Sft = exp{−tf(H)}, Ttf = exp{−tf(K)}, on and examine order properties of the pairs S, T, and Sf, Tf. If , = Lp(X;dv) we define St≽ Tt ≽ 0 if St − Tt and Tt map non-negative functions into non-negative functions. Then for p fixed in the range 1 > p > ∞ we characterize the functions for which St ≽ Tt ≽ 0 implies Sft ≽ Tft ≽ 0 for each Lp(X;dv) and the converse is true for all Lp(X;dv). Further we give irreducibility criteria for the strict ordering of holomorphic semigroups. This extends earlier results for L2-spaces.

We present a new algorithm which uses a cohomological approach to determine the groups of order pn, where p is a prime. We develop two methods to enumerate p-groups using the Cauchy-Frobenius Lemma. As an application we show that there are 10 494213 groups of order 29.

1991 Mathematics subject classification (Amer. Math. Soc.): primary 20D15.

Epimorphic images of compact (algebraically compact) abelian groups are called cotorsion groups after Harrison. In a recent paper, Ph. Schultz raised the question whether “cotorsion” is a property which can be recognized by its small cotorsion epimorphic images: If G is a torsion-free group such that every torsion-free reduced homomorphic image of cardinality is cotorsion, is G necessarily cortorsion? In this note we will give some counterexamples to this problem. In fact, there is no cardinal k which is large enough to test cotorsion.

Some recent papers have revived interest in some questions concerning the motion of a simple pendulum which is oscillating with small angular amplitude under gravity, when the length of the pendulum changes with time in some prescribed manner.

Three differently defined classes of two-symbol sequences, which we call the two-distance sequences, the linear sequences and the characteristic sequences, have been discussed by a number of authors and some equivalences between them are known. We present a self-contained proof that the three classes are the same (when ambiguous cases of linear sequences are suitably in terpreted). Associated with each sequence is a real invariant (having a different appropriate definition for each of the three classes). We give results on the relation between sequences with the same invariant and on the symmetry of the sequences. The sequences are closely related to Beatty sequences and occur as digitized straight lines and quasicrystals. They also provide examples of minimal word proliferation in formal languages.

In this paper we describe a way of representing varieties of algebras by algebras. That is, to each variety of algebras we assign an algebra of a certain type, such that two varieties are rationallv equivalent if and only if the assigned algebras are isomorphic.

The purpose of this paper is to give a more precise form of Theorem 1 of [2], which gives a structure theorem for subgroups of HNN groups; we prove the following.

Let H be a subgroup of the HNN group <A, xi;xiU-ixi-1 = Ui>. Then H is an HNN group whose base is a tree product of groups H ∪ wAw-1 where w runs over a set of double coset representatives of (H,A); the amalgamated and associated subgroups are all of the form H ∊ vUiv-l for some v. We can be more precise about which subgroups occur and about the tree product. We will also obtain stronger forms of other results in [1] and [2].

We establish two-sided bounds for the complexity of two infinite series of closed orientable three-dimensional hyperbolic manifolds, the Löbell manifolds and the Fibonacci manifolds. The manifolds of the two series are indexed by an integer n and the corresponding complexity estimates are both linear in n.

Let k be a positive integer and b a nonzero constant. Suppose that F is a family of meromorphic functions in a domain D. If each function f ∈ F has only zeros of multiplicity at least k + 2 and for any two functions f, g ∈ F, f and g share 0 in D and f(k) and g(k) share b in D, then F is normal in D. The case f ≠ 0, f(k) ≠ b is a celebrated result of Gu.

Sufficient conditons are given for the chaotic behaviour of difference equations defined in terms of continuous mappings in Rn. These conditions are applicable to both difference equations with snap-back repellors and with saddle points. They are applied here to the twisted-horseshoe difference equation of Guckenheimer, Oster and Ipaktchi.

In this paper we introduce the notion of Riesz homomorphism on Archimedean directed partially ordered groups and use it to study the vector lattice cover of such groups.

A semigroup S is called E-inversive if for every a ∈ S ther is an x ∈ S such that (ax)2 = ax. A construction of all E-inversive subdirect products of two E-inversive semigroups is given using the concept of subhomomorphism introduced by McAlister and Reilly for inverse semigroups. As an application, E-unitary covers for an E-inversive semigroup are found, in particular for those whose maximum group homomorphic image is a given group. For this purpose, the explicit form of the least group congruence on an arbitrary E-inversive semigroup is given. The special case of full subdirect products of a semilattice and a group (that is, containing all indempotents of the direct product) is investigated and, following an idea of Petrich, a construction of all these semigroups is provided. Finally, all periodic semigroups which are subdirect products of a semilattice or a band with a group are characterized.

We propose to study a topological property which is not new, but seems not to have been systematically investigated.

A module M over a ring R is κ-projective, κ a cardinal, if M is projective relative to all exact sequence of R-modules 0 → A → B → C → 0 such that C has a generating set of cardinality less than κ. A structure theorem for κ-projective modules over Dedekind domains is proven, and the κ-projectivity of M is related to properties of ExtR (M, ⊕ R). Using results of S. Chase, S. Shelah and P. Eklof, the existence of non-projective и1-projective modules is shown to undecidable, while both the Continuum Hypothesis and its denial (Plus Martin's Axiom) imply the existence of a reduced И0-projective Z-module which is not free.