… is semi-simple; (iii) Every simple ring is semi-… ring" we mean a ring which is not a zero ring
and whose only ideals are itself and the zero ideal. The terms "semi-simple" and "radical ring…

… The form a) of our regularity-definition makes it clear that it coincides with semi-simplicity
whenever the chain-condition holds. Indeed: Assume a). If a is an ri *(O) choose an a * 0 with …

… -ring with regular prime factor rings… ring of a ring R is left 7r-regular, then R is left ττ-regular.
By using this we are able to characterize PI-rings with prime ideals maximal as πregular rings…

… During the conference, Professor JY Kim asked whether R is regular if R is a ring whose
every cyclic left R-module is GP-injective. In this paper, we first prove that a ring R is regular …

… regularity or strong regularity of a ring R is necessary and sufficient condition under which the
ring … strong regularity is the necessary and sufficient condition on a ring R under which the …

… In this paper rings R are associative with identity unless otherwise indicated. All modules …
[12] on semiregularity and partial inverses. In Section 7, we prove that every non-unital ring has …

… rings invented by Nagata, we show (Examples 1,2,3) that (a) <= (b) <= (b') <= (c) do not hold
and that (a) depends on … show that even in local integral domains regularity of a sequence of …

… on such rings under the assumption that the given ring is of bounded index (see [5]). …
We consider first the following ring-property: (*) A ring is nil and of bounded index. Theorem …

… the fact that an idempotent in a ring is also a -‘complemented element” (… rings and distributive
lattices. This has some pathologies [12]; but up to the point of this paper, the discussions on …

… We finish by proving some natural limitations on these … The ring R acts on such vectors by
right multiplication. In this way one can identify the ring R we have constructed with the ring Q …