… A ring is said to be left self injective if it is iniective as the left module over itself. The main …
the following: Let S be a left self injective ring. Then S/N(S) is also left self injective, where N(S) …

… call a ring a left PF-ring if every faithful left module over the ring is … PP-ring is left self-injective,
and also that every QF-ring is left PF. … Each of the simple rings is obviously left self-injective. …

… To prove S is self-injective, we must show that for each right ideal A of S and <p € Homs(A,S…
self-injective ring S where S is a regular ring and the right maximal ring of quotients of C. …

… We call a ring R right PF if every … A ring … Let R be a right self-injective ring satisfying the
conditions in Theorem 1. Let I be a maximal right ideal of R. Then l(I) is a minimal left ideal of R. …

… This theorem shows that any ring B with an injective bimodule E such that B = End EB is …
factor ring R/(0, E) of a self-injective ring, and also leads to new examples of self-injective rings, …

… In this section we show a QF extension of a Gorenstein ring is also a Gorenstein ring. First
we observe the following. Let R, T be rings and F: RM-+TM a functor of the category of left R…

… We were led to the study of such rings by one of … ring of integers modulo n is self-injective
when n =0. Our first main result (Theorem 3.5) is that a commutative ring R is pre-selfinjective if …

… determined under which the maximal right quotient ring of a ring is simple self-injective. All
rings in this paper are associative with 1, and R always denotes a ring. All modules are unital, …

… Generalisations of von Neumann regular rings are … Left self-injective regular, strongly regular
and biregular rings … is either left self-injective regular or a left Artinian local ring such that J2…

… Moreover, as an application, we classify semiprimary rings whose proper homomorphic
images have finite self-injective dimension. AS a consequence, we obtain Faith's [c] and Levy's […