A total category is constructed which has no regular generator although it has an object C such that every object is a regular quotient of a copower of C.

Let (M, °T″) be a compact strongly pseudo-convex CR-manifold with trivial canonical line bundle. Then, in [A-M2], a weak version of the Bogomolov type theorem for deformations of CR-structures was shown by an analogy of the Tian- Todorov method. In this paper, we show that: in the very strict sense, there is a counterexample.

The mapping which assigns to each existence variety of locally inverse semigroups the class of all pseudosemilattices of idempotents of members of is shown to be a complete, surjective homomorphism from the lattice of existence varieties of locally inverse semigroups onto the lattice of varieties of pseudosemilattices.

We consider simple complex Lie algebras extended over the commutative ring C[z,(z — a1)-1, . . . ,(z — an)-1] where a1, . . . ,an ∊ C. We compute the universal central extensions of these Lie algebras and present explicit commutation relations for these extensions. These algebras generalize the untwisted affine Kac-Moody Lie algebras, which correspond to the case n = 1, a 1 = 0.

In this paper it is shown that the maximal spectral type of a general rank one transformation is given by a kind of generalized Riesz product, with possibly some discrete measure.

The quotient field of the ring of invariants of a rational Ga action on Cn is shown to be ruled. As a consequence, all rational Ga actions on C4 are rationally triangulable. Moreover, if an arbitrary rational Ga action on Cn is doubled to an action of Ga × Ga on C2n, then the doubled action is rationally triangulable.

It is shown that the measure algebra on the space 22ω is σ-n-linked for each n ∊ ω.

In this note we extend subharmonic functions defined on closed sets.

In this paper, extending the results in [ 1 ], we establish a necessary and sufficient condition for oscillation in a large class of singular (i.e., the difference operator is nonatomic) neutral equations.

We show that any differentiable involution on a closed manifold whose fixed point set is a disjoint union of odd-dimensional real projective spaces must be a bounding involution.

We introduce the notion of Hankel operators associated with analytic crossed products and consider the Nehari problem in this setting.

It is shown that, in characteristic zero, a finite subgroup of a general linear group is generated by pseudo-reflections if and only if its ring of coinvariants satisfies Poincaré duality.

Cette note corrige un erreur commise dans [Lou, Théorème 4].

In this paper, we use the Lagrange neighbour and our equivalence theorem for primitive ideals to obtain lower bounds which are sharper than those given in the literature for class numbers of real quadratic fields in general, but applied to greatest advantage when d is of ERD type.

Necessary and sufficient conditions are given for a ring to be a union of finitely many proper two-sided ideals.

Suppose that a subset of a finite dimensional lattice has the property that there are many orthogonal tensor products that are almost 1 on the set, then the set is forced to have unusual concentrations of points in small cartesian products.

Among the eight-dimensional stable planes, the compact connected generalized Hughes planes and the geometries induced on the outer points are characterized by the property that these planes admit an effective action of the group SL3 ℂ.

Let n ∊ ℤ+ and R be a ring which possesses a unit element, a left ideal J, and a derivation d such that dn (J) ≠ 0 and dn (r) is 0 or invertible, for all r ∊ J. We prove that either R is primitive, in which case R is Di with 1 ≤ i ≤ n+ 1, where Di is the ring of i × i matrices over a division ring D, or else there exist positive integers i, l and p with p prime and 2 ≤ ipl ≤ n + 1, such that R is where D is a division ring with characteristic p, and furthermore there is a derivation f of Di and a1, a2,..,al ∊ ZDi., the center of Di , such that a ∊ Di then

and

for all 2 ≤ j≤ l

Let F be a field containing a primitive p-th root of unity, let K / F be a cyclic extension with group 〈σ〉 of order pn , and choose a in K. This paper shows how the Galois group of the normal closure of K(a1/p) over F can be determined by computations within K. The key is to define a sequence by applying the operation x ↦ σ(x)/x repeatedly to a. The first appearance of a p-th power determines the degree of the extension and restricts the Galois group to one or two possibilities. A certain expression involving that p-th root and the terms in the sequence up to that point is a p-th root of unity, and the group is finally determined by testing whether that root is 1. When (σ(a)/a G Kp , the results reduce to a theorem of A. A. Albert on cyclic extensions.

Let RM be a nonsingular module such that B = EndR(M) is left nonsingular and has as its maximal left quotient ring, where is the injective hull of RM. Then it is shown that there is a lattice isomorphism between the lattice C(M) of all complement submodules of RM and the lattice C(B) of all complement left ideals of B, and that RM is a CS module if and only if B is a left CS ring. In particular, this is the case if RM is nonsingular and retractable.