To each commutive ring R there is associated a certain commutative regular ring R. The ring
R is in fact an R-algebra. It is shown that RR is never flat, unless R is itself regular. The …

If R is a ring with unit and A is a unitary left R-module, then homological. algebra attaches
three dimensions to A-projec-tive, weak, and injective. By taking the supremum of one of the …

[1; 2; 3]. A module will be said to have dimension n if it has a basis of length w, and if all of its
bases are of the same length. A ring A will be called dimensional if all finitely based …

The fimdam al result of AV Jategaonkar's im ortant paper is th, e following: If is a finitely
generated Noetherian ring, and) r is an essential submoduie of ml! dimens~ Q~ 4.2, then M …

A ring for which every finitely generated right ideal is finitely presented is called a right
coherent ring. Such rings were first studied by Chase i4] as a generalization of right …

1. We suppose that rings have unit elements;" Noetherian" means that the maximum
condition holds for left and right ideals. Let K be a commutative Noetherian integral domain …

Publisher Summary This chapter discusses the global dimension of ore extensions. If R is a
left and right noetherian and of a finite left global dimension, a necessary condition for …

The purpose of this note is to prove the following result. Theorem 1. Let n be an integer
greater than zero. There exists a prime Noetherian ring R of Krull dimension n+ 1 and a …

A left and right Noetherian local ring of global dimension 3 is a domain. It is well known that
a commutative Noetherian local ring of finite global dimen-sion is an integral domain. We …

The notion of Krull dimension of an R-module which is now one of the basic tools in the
theory of right Noetherian rings, see [5],[9] and [19], was first introduced by Rentschler and …