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- W1586080445 abstract "ℤ being an integral domain, for each multiplicative system S ⊂ ℤ, the ring of quotients identified with a subring with identity of Q, the rational numbers of the form ( frac{m}{s} ) with m ∈ ℤ and s ∈ S. Now, if A is a subring of Q and 1 ∈ A let ( {{S}_{A}} = left{ {n in mathbb{Z}left| {frac{1}{n} in A} right.} right} ). Obviously, S A is a multiplicative system and ( {{mathbb{Z}}_{{{{S}_{A}}}}} subseteq mathbb{Q} ). Conversely, if ( frac{m}{n} in A ) with (m;n) = 1 let u, v ∈ such that um + vn = 1. Then ( ufrac{m}{n} + v = frac{1}{n} in A ) and hence A ∈ ℤ SA ." @default.
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- W1586080445 date "1998-01-01" @default.
- W1586080445 modified "2023-10-17" @default.
- W1586080445 title "Rings of Quotients" @default.
- W1586080445 doi "https://doi.org/10.1007/978-94-015-9004-4_15" @default.
- W1586080445 hasPublicationYear "1998" @default.
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