The term The Theory of Rings seems first used as title of a book by Jacobson [43], and in his
preface Jacobson asserts that the theory that forms the subject of the book had its beginning …

Page 1 Mathematical Society e Note Series 27 w Field structions COHN Page 2 HING ET ALMA
MATER CANTA BRIGIA SACRA CAMBRIDGE UNIVERSITY PRESS: SYNDICS LIBRARY …

It has been recently observed that fundamental aspects of the classical theory of
factorization can be greatly generalized by combining the languages of monoids and …

We combine the language of monoids with the language of preorders so as to refine some
fundamental aspects of the classical theory of factorization and prove an abstract …

The problem of diagonalization of matrices is a classic one. Its prototype is the Gauss
theorem on the equivalence of arbitrary matrix over the field to a diagonal matrix with ones …

In a 1968 issue of the Proceedings, PM Cohn famously claimed that a commutative domain
is atomic if and only if it satisfies the ascending chain condition on principal ideals (ACCP) …

Abstract A right R-module C is proper cyclic in case R→ C→ 0 is exact but 0→ R→ C→ 0 is
not. A ring R is a ring PCI ring if every proper cyclic right R-module is injective (PC⇒ I ring”) …

Abstract Techniques of Eilenberg, Nakayama, and Nagao are used to obtain results on the
global dimension of the ring R∕ I where I is an eventually idempotent ideal. We also …

Jategaonkar (5) has constructed a class of rings which can be used to provide
counterexamples to problems concerning unique factorization in non-commutative domains …

A natural generalization is to consider rings in which all relations (1.1) are trivial, for a fixed
n. It turns out that such rings share many of the properties of semifirs, strong GE-rings or …