The theory of rings of quotients has its origin in the work of (j). Ore and K. Asano on the
construction of the total ring of fractions, in the 1930's and 40's. But the subject did not really …

Introduction. All rings in this paper are commutative with identity element, and all subrings
possess the identity element of the containing ring. An overring of an integral domain …

The development of a general theory of rings of quotients may be said to have started with
the construction by Johnson [1] of the maximal ring of quotients Q max of a non-singular ring …

A pair of integral domains (A, B) is a normal (resp., QR-) pair provided that A is a subring of B
and all intermediate rings are normal in B (resp., rings of quotients of A). The special case of …

1. Introduction. If A is an integral domain and S is a subset of A not containing zero, then one
can form the quotient ring As which lies between A and its quotient field. It is well known that …

In this chapter we shall make a study of rings satisfying certain ascending chain conditions.
In the non-commutative case-and this is really the only case with which we shall be …

This is an abridged edition of the author's previous two-volume work, Ring Theory, which
concentrates on essential material for a general ring theory course while ommitting much of …

The viability of the theory of commutative rings is evident from the many papers on the
subject which are published each month. This is not surprising, considering the many …

By an F-ring we shall mean a 1-dimensional ring 0 such that O [x] is not 2-dimensional (ie,
the proposed assertion that O [x] is necessarily 2-< iimensional fails). Given an F-ring, we try …

This book has two predominant objectives. On the one hand, the fundamental concepts of
the theory of modules and rings are presented, for which the presentation is set out in detail …