The structure of rings without proper essential left ideals is described, as well as that of rings
having an essential minimal left ideal. _ In the recent radical theoretical paper [4] …

In this paper we are mainly concerned with rings satisfying the descending chain condition
(dcc) on left principal ideals. Such rings are called left coperfect rings in this paper. When left …

This paper determines the structure of finite rings whose two sided ideals are principal as left
ideals, and as right ideals. Such rings will be called principal ideal rings. Although finite …

In non-associative ring theory the lattice of left ideals has not proven nearly as useful a tool
as in the associative theory. A partial reason for this is that given an element x in a non …

In oar thesis [7] and in A. i (~ RT~ sz--O. STEINFELD [6] we have given some new
characterizations of semisimple artinian rings.(See also A. KERT~ SZ [5].) In this paper we …

One finds in the literature a thorough-going discussion of rings without radical and with
minimal condition for left ideals (semi-simple rings). For the structure of a ring whose …

In the theory of semisimple rings (ie rings with minimum condition on left ideals and without
nonzero nilpoterit left ideals) the most important theorem, due to WEDDERBURN--ARTIN …

In what follows under a ring we always mean an associative one. The main object of this
paper is to describe the structure of nil rings with minimum condition on principal right ideals …

A ring with identity is said to be a local ring if it contains a unique maximal right ideal [2; 751.
This implies that the unique maximal right ideal is also the unique maximal ideal. But rings …

Maximal left ideals in matrix rings were studied by Stone [10]. Similar results are not
necessarily valid in the general near-ring case and one of the objectives of this paper is to …