# Rings of quotients

Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 449)

## Abstract

Let T be a set of elements in a ring A. The set T is right permutable if for any aA and tT, there exist bA, uT such that au = tb. A multiplicative set in a ring A is any subset T of A such that 1 ∈ T,0 ∉ T and T is closed under multiplication. A completely prime ideal in a ring A is any proper ideal B such that A\B is a multiplicative set (i.e. A/Bis a domain). A minimal prime ideal (resp. minimal completely prime ideal) in a ring A is any prime (resp. completely prime) ideal P such that P contains no properly any other prime ideal (resp. completely prime ideal) of A. Let I be any proper ideal of a ring A. The set of all elements aA such that a + I is a regular element of A/I is denoted by c(I). In particular, c(0) is the set of all regular elements of A.

## Keywords

Prime Ideal Division Ring Regular Element Semiprime Ring Minimal Prime Ideal
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Authors and Affiliations

1. 1.Moscow Power Engineering InstituteTechnological UniversityMoscowRussia