Abstract
Let T be a set of elements in a ring A. The set T is right permutable if for any a ∈ A and t ∈ T, there exist b ∈ A, u ∈ T 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 a ∈ A 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.
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© 1998 Springer Science+Business Media Dordrecht
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Tuganbaev, A.A. (1998). Rings of quotients. In: Semidistributive Modules and Rings. Mathematics and Its Applications, vol 449. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5086-6_5
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DOI: https://doi.org/10.1007/978-94-011-5086-6_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6136-0
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