On ideals consisting entirely of zero divisors

An ideal Iin a commutative ring Ris called a z°-ideal if Iconsists of zero-divisors and for each a? Ithe intersection of all minimal prime ideals containing ais contained in I.We prove that in a large class of rings, containing Noetherian reduced rings, Zero-dimensional rings, polynomials over reduced rings and C(X), every ideal consisting of zero-divisors is contained in a prime z°-ideal. It is also shown that the classical ring of quotients of a reduced ring is regular if and only if every prime z°-ideal is a minimal prime ideal and the annihilator of a f.g. ideal consisting of zero-divisors is nonzero. We observe that z°-ideals behave nicely under contractions and extensions.     

Rings with a certain condition on subsemigroups

In what followsK denotes a field. An algebra means an asociative algebra, modules over algebras are right ones.     

The probability of generating certain profinite groups by two elements

In this paper we consider the question of finite generation of profinite groups. We study the class of profinite groups which are inverse limits of wreath products of alternating groups of degree ≥5. We prove that the probability of generating such inverse limits by two elements is strictly positive and tends to 1 as the degree of the first factor tends to infinity. Our method of analysis requires a survey of the maximal subgroups of iterated wreath products of alternating groups. Although we have been unable to classify these precisely we do obtain upper bounds for the number of conjugacy classes of maximal subgroups which we believe to be of independent interest. The author is grateful for financial support received under the FCO-award scheme.     

Local Rings of Rings of Quotients

The aim of this paper is to characterize those elements in a semiprime ring R for which taking local rings at elements and rings of quotients are commuting operations. If Q denotes the maximal ring of left quotients of R, then this happens precisely for those elements if R which are von Neumann regular in Q. An intrinsic characterization of such elements is given. We derive as a consequence that the maximal left quotient ring of a prime ring with a nonzero PI-element is primitive and has nonzero socle. If we change Q to the Martindale symmetric ring of quotients, or to the maximal symmetric ring of quotients of R, we obtain similar results: an element a in R is von Neumann regular if and only if the ring of quotients of the local ring of R at a is isomorphic to the local ring of Q at a. Partially supported by the Ministerio de Educación y Ciencia and Fondos Feder, jointly, trough projects MTM2004-03845, MTM2007-61978 and MTM2004-06580-C02-02, MTM2007-60333, by the Junta de Andalucía, FQM-264, FQM336 and FQM02467 and by the Plan de Investigación del Principado de Asturias FICYT-IB05-017.     

Generating elements and defining relations for symplectic groups over certain rings

We determine the generating elements and defining relations for symplectic groups over local rings in which each finitely generated right ideal is principal.     

ON ORDER RINGS OF SEMI-PRIMARY RINGS

The main results of this paper are stated as follows.Let R be an orderring in thesemi-primary ring Q.Suppose that R satisfies the maximal condition for nil right ideals ofR,Then we have(i)if an ideal I of R has a finite length as right R-module,then I alsohas a finite length as left R-module;(ii)denote by A(R)the Artinian radical of R,andN the nil radical of R,then A(R)+N/N=A(R/N),if R satisfies the commutative condi-tion on the zero product of prime ideals of B.     

Stress-optimal regimes for heating a piecewise-homogeneous glass shell of revolution consisting of elements of different geometric shapes

By using numerical methods we construct the solution of the problem of determining the stress-optimal regimes (by the criterion of minimizing the maximal normal stresses) for heating a piecewise-homogeneous shell consisting of a cylindrical shell and a conical shell coupled with it that is closed at the vertex. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.