Heavy tails for an alternative stochastic perpetuity model

In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten (1973) and Goldie (1991) all discount factors in the model are mutually independent. We prove that the tails of the distribution of this model are regularly varying both in the univariate and multivariate cases. Due to the additional randomness in the model the tails are not pure power laws as in the Kesten–Goldie setting but involve a logarithmic term.     

Essential Ideals in Rings of Measurable Functions

In this article, we study essential ideals, socle, and some related ideals of rings of real valued measurable functions. We also study the Goldie dimension of rings of measurable functions.     

Two Open Questions On Goldie Extending Modules

Five open questions on Goldie extending modules were posed by Akalan et al. [1 Akalan , E. , Birkenmeier , G. F. , Tercan , A. ( 2009 ). Goldie extending modules . Comm. Algebra 37 : 663 – 683 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. The first one and the second one are considered in this article. It is shown that a 𝒢-extending module M with (C ₃) is 𝒢⁺-extending. Moreover, let M = M ₁ ⊕ M ₂ be a direct sum of 𝒢-extending modules, where M satisfies (C ₃) and M ₁ is M ₂-ojective (or M ₂ is M ₁-ojective), then M is 𝒢-extending. Other sufficient conditions for a direct sum of 𝒢-extending modules to be 𝒢-extending are obtained.     

某些左零化子满足归纳条件的环

本文研究了某些特殊左零化子满足归纳条件的环的结构,得到:如果R是诣零环,P是使P半单环不含非零幂零理想的根性质,R为P根环的一个刻画。并对Goldie环的条件作了研究,得到了更一般的结果。     

Partial Crossed Products and Goldie Rings

In this paper we consider the transfer of the property of being a left Goldie ring between a ring A and its partial crossed product A*_α G by a twisted partial action α of a group G on A.     

On right G-semilocal rings

The notion of semilocal ring is extended to the classes of right G-semilocal and right N-semilocal rings. We explore the algebraic properties of such classes and study their relations with many other rings such as clean, exchange and I-finite rings. Localization of right G-semilocal rings is considered.     

Rings Whose Modules Have Grade Zero

In this paper, we prove that R is a two-sided Artinian ring and J is a right annihilator ideal if and only if (i) for any nonzero right module, there is a nonzero linear map from it to a projective module; (ii) every submodule of RR is not a radical module for some right coherent rings. We call a ring a right X ring if Homa(M, R) = 0 for any right module M implies that M = 0. We can prove some left Goldie and right X rings are right Artinian rings. Moreover we characterize semisimple rings by using X rings. A famous Faith‘s conjecture is whether a semipimary PF ring is a QF ring. Similarly we study the relationship between X rings and QF and get many interesting results.     

Goldie Conditions for Ore Extensions over Semiprime Rings

Let R be a ring, σ an injective endomorphism of R and δ a σ-derivation of R. We prove that if R is semiprime left Goldie then the same holds for the Ore extension R[x;σ,δ] and both rings have the same left uniform dimension. Presented by S. Montgomery Mathematics Subject Classification (2000) 16S90. Jerzy Matczuk: Supported by the Flemish–Polish bilateral agreement BIL 01/31.     

A classification of prime segments in simple artinian rings

Let be a simple artinian ring. A valuation ring of is a Bézout order of so that is simple artinian, a Goldie prime is a prime ideal of so that is Goldie, and a prime segment of is a pair of neighbouring Goldie primes of A prime segment is archimedean if is equal to it is simple if and it is exceptional if In this last case, is a prime ideal of so that is not Goldie. Using the group of divisorial ideals, these results are applied to classify rank one valuation rings according to the structure of their ideal lattices. The exceptional case splits further into infinitely many cases depending on the minimal so that is not divisorial for

     

On fusible rings

We answer in negative two of questions posed in Ghashghaei and McGovern. We also establish a new characterization of semiprime left Goldie rings by showing that a semiprime ring R is left Goldie iff it is regular left fusible and has finite left Goldie dimension.