A module is extending (or CS, C1) if every complement submodule is a direct summand or,
equivalently, every submodule is essential in a direct summand. The terms extending and …

Abstract A module M satisfies (C< sub> 11</sub>) if every submodule of M has a
complement which is a direct summand of M. It is shown that there exists a commutative …

The purpose of these notes is to provide a brief introduction to the subject of localizing at
prime ideals in noncommutative Noetherian rings. The aim is to present material connected …

A module is said to be $ PI $-extending provided that every projection invariant submodule
is essential in a direct summand of the module. In this paper, we focus on direct summands …

This article is a survey of some aspects of the K-theory of Noetherian rings. Mainly we shall
be concerned with calculating the (Quillen) K-groups for specific Noetherian rings but we …

Let $ R [unk] S $ be an embedding of associative noetherian rings such that $ S $ is finitely
generated as a right $ R $-module. There is a correspondence from the prime spectrum of …

The theory of finitely generated projective modules is a classical topic in ring theory inspired
by rich connections with K-theory, geometry and algebraic topology. However, it is often …

This paper continues our study, begun in [MS], of the relationship between the prime ideals
of an algebra A and of a subalgebra R such that R⊂ A is a faithfully flat H-Galois extension …

It is shown that for every positive integer r there is a (left and right) noetherian domain, of
Krull dimension 1, that has an indecomposable projective module of uniform‐rank r. Direct …

Finite ring extensions of Noetherian rings with certain restrictions on the corresponding trace
ideals are studied. This setting includes finite free extensions and extensions arising from …