Rings of quotients

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


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.


Prime Ideal Division Ring Regular Element Semiprime Ring Minimal Prime Ideal 
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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  1. 1.Moscow Power Engineering InstituteTechnological UniversityMoscowRussia

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