Abstract. We give a polynomial-time algorithm of computing the classical Hurwitz numbers Hg,d, which were defined by Hurwitz 125 years ago. We show that the generating series of Hg,d for any fixed g > 2 lives in a certain subring of the ring of formal power series that we call the Lambert ring. We then define some analogous numbers appearing in enumerations of graphs, ribbon graphs, and in the ...

Abstract Let D be a finite-dimensional division algebra over its center and R = [ t ; ? , ? ] skew polynomial ring. Under certain assumptions on the ring of central quotients ( ) { f / g | ? ], C ])} is simple with reduced norm N . We calculate for some polynomials investigate when how reducibility reflects

We consider the task of learning a ring in a distributed way: each node of an unknown ring has to construct a labeled map of it. Nodes are equipped with unique labels. Communication proceeds in synchronous rounds. In every round every node can send arbitrary messages to its neighbors and perform arbitrary local computations. We study tradeoffs between the time (number of rounds) and the cost (n...

Fuchs [6] called a partially-ordered integral domain, say D, division closed if it has the property that whenever a > 0 and ab > 0, then b > 0. He showed that if D is a lattice-ordered division closed field, then D is totally ordered. In fact, it is known that for a lattice-ordered division ring, the following three conditions are equivalent: a) squares are positive, b) the order is total, and ...

(1) If $R$ is an affine algebra of dimension $d\geq 4$ over $\overline{\mathbb{F}}_{p}$ with $p>3$, then the group structure on ${\rm Um}_d(R)/{\rm E}_d(R)$ nice. (2) a commutative noetherian ring 2$ such that E}_{d+1}(R)$ acts transitively Um}_{d+1}(R),$ Um}_{d+1}(R[X])/{\rm E}_{d+1}(R[X])$

Throughout this paper, R will represent an associative ring with center Z(R). A ring R is n-torsion free, where n > 1 is an integer, in case nx = 0, x ∈ R implies x = 0. As usual the commutator xy− yx will be denoted by [x, y]. We will use basic commutator identities [xy,z] = [x,z]y + x[y,z] and [x, yz] = [x, y]z+ y[x,z]. Recall that a ring R is prime if aRb = (0) implies that either a = 0 or b...

Consider in the space C with the coordinates x{ , x2, x3 the surface X defined by the equation x\ + x\ + x\ = 0. We prove the following theorem: T H E O R E M 1. Let D{X) be the ring of regular differential operators on X, and Da the ring of germs at the point 0 of analytic operators on X. Then 1°. the rings D(X) and Da are not Noetherian; 2°. for any natural number k the rings D{X) and Da are ...

Several authors have studied the question of when the monoid ring DM of a monoid M over a ring D is a right and/or left fir (free ideal ring), a semifir, or a 2-fir (definitions recalled in §1). It is known that for M nontrivial, a necessary condition for any of these properties to hold is that D be a division ring. Under that assumption, necessary and sufficient conditions on M are known for D...

THE TITLE COMPOUND [SYSTEMATIC NAME: (R)-2-trichloro-methyl-3a,3b,7a,8a-tetra-hydro-5H-pyrano[2',3':4,5]furano[2,3-d][1,3]dioxol-5-one], C(9)H(7)Cl(3)O(5), a triyclic system that contains a central α-d-furan-ose ring cis-fused with a dioxolane ring as well as a δ-lactone ring, exhibits a twisted conformation. The CCl(3) group has an axial orientation. The furan-ose ring approximates an envelope...