Skew-gentle algebras are a generalisation of the well-known class of gentle algebras with which they share many common properties. In this work, using non-commutative Gröbner basis theory, we show that these algebras are strong Koszul and that the Koszul dual is again skew-gentle. We give a geometric model of their bounded derived categories in terms of polygonal dissections of surfaces with orbifold points, establishing a correspondence between curves in the orbifold and indecomposable objects. Moreover, we show that the orbifold dissections encode homological properties of skew-gentle algebras such as their singularity categories, their Gorenstein dimensions and derived invariants such as the determinant of their q-Cartan matrices.

Let be either a C*-algebra (with norm ∥ ∥) or a symmetric ideal of operators on a Hilbert space (with norm denoted by σ). Let a1…, an be self-adjoint elements, and let a0 = .

Suppose that a complex manifold M is locally embedded into a higher-dimensional neighbourhood as a submanifold. We show that, if the local neighbourhood germs are compatible in a suitable sense, then they glue together to give a global neighbourhood of M. As an application, we prove a global version of Hertling–Manin's unfolding theorem for germs of TEP structures; this has applications in the study of quantum cohomology.

We study the moduli space of pluriregular threefolds of general type with K3X=8, 10, 12 and p_g(X)=5 and whose canonical map is a finite morphism onto a smooth quadric Q⊂ ℙ4[Copf].

In this paper, we shall be concerned with the solution of triple integral equations of the type

where M−1 is the inverse Mellin transform, nis a positive integer, and — 1 < Res < 0. The use of these equations will be illustrated by their application to two well-known problems in the mathematical theory of elasticity and further applications will be reported later.

Answering a question of Hoffmann and of Kambites, an example is exhibited of a finitely generated semigroup $S$ such that $S$ embeds in a group and $S$ is not automatic, but the universal group of $S$ is automatic.

Several properties are known to be inherited from the derived factor group of a group G by other factors Γi = γi(G)/γi + 1(G) of the lower central series. Derek Robinson proved [1] that the denning property of any class of groups which is closed under the forming of homomorphic images of tensor products is so inherited. Possibilities for here include the following classes.

Let (R, M) be a local ring and let R* be the M-adic ring completion of R. It is well known that R is a regular local ring if and only if R* is a regular local ring. The purpose of the note is to show that this result is essentially a consequence of a more general theory concerning local Noether lattices which was developed in [6].

In this paper we present sufficient conditions for all trajectories of the system to cross the vertical isocline h(y) = F(x), which is very important in the global asymptotic stability of the origin, oscillation theory and existence of periodic solutions. Also we give sufficient conditions for all trajectories which start at a point on the curve h(y) = F(x), to cross the y-axis which is closely connected with the existence of homoclinic orbits, stability of the zero solution, oscillation theory and the centre problem. The obtained results extend and improve some of the authors' previous results and some other theorems in the literature.

In a recent illuminating paper, June M. Parker [5] discussed Choquet integral representations of comonotonic additive functionals and related concepts. In our paper we provide a generalization of the Choquet integral and use this to obtain an integral representation for comonotonic additive operators.

It is shown that if C1 and C2 are maximal abelian self-adjoint subalgebras (masas) of C*-algebras A1 and A2, respectively, then the completion C1 ⊗ C2 of the algebraic tensor product C1 ⊙ C2 of C1 and C2 in any C*-tensor product A1 ⊗βA2 is maximal abelian provided that C1 has the extension property of Kadison and Singer and C2 contains an approximate identity for A2. Examples are given to show that this result can fail if the conditions on the two masas do not both hold. This gives an answer to a long-standing question, but leaves open some other interesting problems, one of which turns out to have a potentially intriguing implication for the Kadison-Singer extension problem.

We start here the study of some algebraic varieties related to cluster algebras. These varieties are defined as the fibres of the projection map from the cluster variety to the affine space of coefficients. We compute the number of points over finite fields on these varieties, for all simply laced Dynkin diagrams. We also compute the cohomology with compact support in some cases.

Using a variation on the concept of a CS module, we describe exactly when a simple ring is isomorphic to a ring of matrices over a Bézout domain. Our techniques are then applied to characterise simple rings which are right and left Goldie, right and left semihereditary.

Suppose E is an elliptic curve over $\Bbb Q$, and p>3 is a split multiplicative prime for E. Let q ≠ p be an auxiliary prime, and fix an integer m coprime to pq. We prove the generalised Mazur–Tate–Teitelbaum conjecture for E at the prime p, over number fields $K\subset \Bbb Q\big(\mu_{{q^{\infty}}},\;\!^{q^{\infty}\!\!\!\!}\sqrt{m}\big)$ such that p remains inert in $K\cap\Bbb Q(\mu_{{q^{\infty}}})^+$. The proof makes use of an improved p-adic L-function, which can be associated to the Rankin convolution of two Hilbert modular forms of unequal parallel weight.

In two recent papers [1, 2] the Barnes integral for the E-functions was employed to sum a number of infinite series of E-functions. In §2 of this paper, by making use of the multiplication formula for the gamma function, the method is extended to series of E-functions of a different type.

Dedicated to the memory of Professor Katsutoshi Takahashi

In this paper, we introduce p-hyponormal tuples in the sense of D. Xia. Furthermore we extend Putnam’s inequality to these tuples and show an equivalence relation of two spectra.

V-rings and their generalisations have been studied extensively in recent years [2], [3], [5],[6], [7]. All the rings we consider will be associative rings with 1 ≠ 0 and all the modules considered will be unitary left R-modules. All the concepts will be left-sided unless otherwise mentioned. Thus by an ideal in R we mean a left ideal of R. A ring R is called a V-ring (respectively a GV-ring) if every simple (resp. simple, singular) module is injective. An R-module M is called p-injective if any homomorphism f: I → M with I a principal left ideal of R can be extended to a homomorphism g: R → M. A ring R is called a p-V-ring (resp. a p-V'-ring) if every simple (resp. simple, singular) module over R is p-injective. The object of the present paper is to introduce torsion theoretic generalizations of p-V-rings and prove results similar to those obtained by Yue Chi Ming about p-V-rings and p-V'-rings [6], [7]. For any M ∈ R-mod, J(M) will denote the Jacobson radical of M and Z(M) the singular submodule of M. For any λ ∈ R, we denote the left annihilator { r ∈ R| rλ =0 } of λ in R by l(λ).

Let I denote the interval [0,1] in its usual topology and let S = S(I) be the semigroup of continuous mappings of I into itself with function composition as the semigroup operation. In a survey talk given at Oberwolfach in 1989 (see [5]), K. D. Magill Jr. pointed out that some elementary algebraic properties of S are still unknown. We shall answer one of the questions he raised (which appears as Problem 4.6 in [5] and which he had asked earlier, as long ago as 1975 [3]) by showing that S has infinitely many distinct two-sided ideals. In fact, we shall produce an infinite descending sequence of distinct ideals. As Magill points out, this also solves his Problem 4.5: S has infinitely many distinct congruences. We believe that S must have c distinct ideals, but we have been unable to prove this.

In this paper, will always denote a local class of locally finite groups, which is closed with respect to subgroups, homomorphic images, extensions, and with respect to cartesian powers of finite -groups. Examples for x are the classes L ℐπ of all locally finite π-groups and L(ℐπ ∩ ) of all locally soluble π-groups (where π is a fixed set of primes). In [4], a wreath product construction was used in the study of existentially closed -groups (=e.c. -groups); the restrictive type of construction available in [4] permitted results for only countable groups. This drawback was then removed partially in [5] with the help of permutational products. Nevertheless, the techniques essentially only permitted amalgamation of -groups with locally nilpotent π-groups. Thus, satisfactory results could be obtained for Lp-groups (resp. locally nilpotent π-groups) [6], while the theory remained incomplete in all other cases.

We derive a finite normal series for the group {\rm Aut}\nolimits _*(X\;\!) of self-homotopy equivalences which induce identity automorphisms of homology groups, where X is a countable, simply-connected and finite-dimensional CW-complex.