Semi-primary hereditary rings

A semi-primary hereditary ring Σ, with radicalM and residue ring Γ=Σ/M, is uniquely determined by Γ and a Γ-bimoduleA=M/M ², whenever Σ admits a splitting Σ=Γ+A+M ².     

A note on hereditary rings

Herediticity of tensor products of hereditary rings is described and used to characterize certain hereditary prime factor rings of polynomial rings over hereditary P.I. rings.     

一类广义遗传环

称环R为左亚遗传环，如果内射左R－模的商模是FG－内射的，给出了左亚遗传环的一些刻划，给出了左亚遗传环的半单环的条件，并研究了左亚遗传环的一些性质。     

Group rings which are G-Dedekind prime rings

Let R be a commutative Noetherian domain and A be a polycyclic-by-finite group. In this paper, it is determined, in terms of properties of R and A when the group ring R[A] is a G-Dedekind prime ring.     

A new characterisation of hereditary pi rings

In this paper we prove a new characterisation of hereditary PI rings, namely we show that a Noetherian, but not Artinian, PI ringR that is an order in an Artinian ring splits into a direct sum of an Artinian ring of finite representation type and hereditary semiprime rings if and only if all its proper Artinian factor rings are of finite representation type. We also show, through examples, that the above characterisation does not hold for some more general settings. Supported by the EC via TMR-Fellowship ERB4001GT63713.     

Some minimal rings related to 2-primal rings

In a paper on the taxonomy of 2-primal rings, examples of various types of rings that are related to commutativity such as reduced, symmetric, duo, reversible and PS I were given in order to show that the ring class inclusions were strict. Many of the rings given in the examples were infinite. In this paper, where possible, examples of minimal finite rings of the various types are given. Along with the rings in the previous taxonomy, NI, abelian and reflexive rings are also included.