Given amalgams of semigroups [U; Ti] and [U;Si] with U⊆Ti⊆Si, it was proved by Howie in [6] that need not be embedded in . We use the homological techniques developed by Renshaw in [7, 9] and study three new conditions each of which imply the embeddability of the above free products.

We are concerned with the following problem. Let F be a Fréchet Montel space and let E be a Fréchet space with a certain property (P). When does it follow that the complete projective tensor product has the property (P)? (We consider the following properties: being Montel, reflexive, satisfying the density condition.) In this paper we provide a positive answer if F is a Montel generalized Dubinsky sequence space with decreasing steps.

It is shown that a ring R is a π-regular ring with no infinite trivial subring if and only if R is a subdirect sum of a strongly regular ring and a finite ring. Some other characterizations of such a ring are given. Similar result is proved for a periodic ring. As a corollary, it is shown that every δ-ring is a subdirect sum of a Unite ring and a commutative ring. This was conjectured by Putcha and Yaqub.

The aim of the paper is to prove the Theorem: Let M be a surface in the euclidean space E3 which is diffeomorphic to the sphere and suppose that all geodesies of M are congruent. Then M is a euclidean sphere.

The kernel–trace approach to congruences on a regular semigroup S can be refined by introducing the left and right traces. This induces eight operators on the lattice of congruences on S: t1, k, tr,; Tt, K, Tr; t, T. We describe the lattice of congruences on S generated by six 3-element subsets of the set {ωt1, ωk, ωtr, εTt, εK, εTr} where ω and ε denote the universal and the equality relations. This is effected by means of a diagram and in terms of generators and relations on a free distributive lattice, or a homomorphic image thereof. We perform the same analysis for the lattice of congruences on S generated by the set {εK, ωk, εT, ωt}.

A study is made of the length L(h, k) of the continued fraction algorithm for h/k where h and k are co-prime polynomials in a finite field. In addition we investigate the sum of the degrees of the partial quotients in this expansion for h/k, h, k in . The above continued fraction is determined by means of the Euclidean algorithm for the polynomials h, k in .

Implicit operations (new operations commuting with all old homomorphisms) on pseudovarieties have been shown to play an important role in the study of these classes. They may be used to axiomatize sub-pseudovariaties and to describe recognizable subsets of (relatively) free objects. This paper presents a case study for the pseudovariety CS consisting of all finite simple semigroups. Based on a result of profinite group theory, a structural description of semigroups of implicit operations on finite simple semigroups is used to deduce that CS is join-irreducible.

We consider discrete convolution operators whose range is the k-dimensional space spanned by the translates of a single function. Examples of include the space of trigonometric polynomials, periodic polynomial splines and trigonometric splines. The eigenfunctions of these operators corresponding to the nonzero eigenvalues are independent of α, and they form an orthogonal basis for . The limiting behaviour of as α, k→∞, is also considered. The corresponding limiting semigroups are computed explicitly.

Some properties of polynomials associated with strong distribution functions are given, including conditions for the polynomials to satisfy a three term recurrence relation. Strong distributions that are extensions to the four classical distributions are given as examples.

The class of prime Noetherian v-H orders is a class of Noetherian prime rings including the commutative integrally closed Noetherian domains, and the hereditary Noetherian prime rings, and designed to mimic the latter at the level of height one primes. We continue recent work on the structure of indecomposable injective modules over Noetherian rings by describing the structure of such a module E over a prime Noetherian v-H order R in the case where the assassinator P of E is a reflexive prime ideal. This description is then applied to a problem in torsion theory, so generalising work of Beck, Chamarie and Fossum.

Two commutative Banach algebras A and B are said to be similar if there exists a Banach algebra D such that [xD]− = D for some x in D, and two one-to-one continuous homomorphisms φ:D→A and ψ:D→B such that φ(D) is a dense ideal of A and ψ(D) a dense ideal of B.

We prove in this paper that the Volterra algebra is similar to A0/e-z A0 where A0 is the commutative uniform, separable Banach algebra of all continuous functions on the closed right-hand half plane , analytic on H and vanishing at infinity. We deduce from this result that multiplication by an element of A0/e-z A0 is a compact mapping.

Let R be a ring and G a polycyclic-by-finite group. In this paper, it is determined, in terms of properties of R and G, when the group ring R[G] is a prime Krull order and when it is a price v-HC order. The key ingredient in obtaining both characterizations is the first author's earlier study of height one prime ideals in the ring R[G[.

By a divisibility semigroup we mean an algebra (S,., ∧) satisfying (Al) (S,.) is a semigroup; (A2) (S, ∧) is a semilattice; (A3) .

A divisibility semigroup is called representable if it admits a subdirect decomposition into totally ordered factors.

In this paper various types of representable divisibility semigroups are investigated and characterized, admitting a representation in general or even a special decomposition, like subdirect sums of archimedean factors, for instance.

An isomorphism (as groups) is established between an arbitrary connected module over a structural matrix near-ring and a direct sum of appropriate modules over the base near-ring. This isomorphism leads to a characterization of the 2-primitive ideals of a structural matrix near-ring.

The paper deals with superlinear elliptic boundary value problems depending on a parameter. Given appropriate hypotheses concerning the asymptotic behaviour of the nonlinearity, we prove lower bounds on the number of solutions. The results generalize a theorem due to Lazer and McKenna within the framework of quasi-Banach spaces of Besov and Triebel-Lizorkin spaces.

A ring R is prime essential if R is semiprime and for each prime ideal P of R, P ∩ I ≠0 whenever I is a nonzero two-sided ideal of R. Examples of prime essential rings include rings of continuous functions and infinite products modulo infinite sums. We show that the class of prime essential rings is closed under many familiar operations; in particular, we consider polynomial rings, matix rings, fixed rings and skew group rings. Also, we explore the relationship between prime essential rings and special radical classes, and we demonstrate how prime essential rings can be used to construct radical classes which are not special.

A short proof of Chow's generalization of Widder's inequality and generalizations of some related Hardy's results are given.

Let X be an infinite set and S be a transformation semigroup on X invariant under conjugations by permutations of X. Such S is termed x-normal. In the paper, we describe elements of a x-normal semigroup S of one-to-one transformations.

A one parameter family of algorithms is studied, which contains both the arithmetic-geometric mean of Gauss and its generalization by Borchardt, recently studied by J. and P. Borwein. We prove that the presence of an asymptotic formula for such an algorithm is, in view of the Poisson summation formula, equivalent to the vanishing of certain integrals. In the case of Gauss and Borchardt the latter involve theta functions. Finally, we investigate the question of convergence of the algorithm for complex values, thereby generalizing the corresponding result of Gauss.

In this paper we investigate totally geodesic surfaces in hyperbolic 3-manifolds. In particular we show that if M is a compact arithmetic hyperbolic 3-manifold containing an immersion of a totally geodesic surface then it contains infinitely many commensurability classes of such surfaces. In addition we show for these M that the Chern-Simons invariant is rational.

We also show, that unlike the figure-eight knot complement in S3, many knot complements in S3 do not contain an immersion of a closed totally geodesic surface.