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A general theory of Fountain-Gould quotient rings. (English) Zbl 0811.16023

The quotient rings of the title were introduced by J. Fountain and V. Gould [Commun. Algebra 18, 3085-3110 (1990; Zbl 0719.16022)], and their properties were studied there and in a series of subsequent papers by these authors. In the present paper the Fountain-Gould quotient ring is compared with the maximal left quotient ring of Utumi – when it exists, the former is a subring of the latter – and with the classical left quotient ring – when both exist, they are isomorphic.

MSC:

16S90 Torsion theories; radicals on module categories (associative algebraic aspects)
16U20 Ore rings, multiplicative sets, Ore localization

Citations:

Zbl 0719.16022
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References:

[1] FOUNTAIN J., GOULD V.: Orders in rings without identity. Comm. Algebra 18 (1990), 3085-3110. · Zbl 0719.16022
[2] FOUNTAIN J., GOULD V.: Orders in regular rings with minimal condition for principal right ideals. Comm. Algebra 19 (1991), 1501-1527. · Zbl 0726.16007
[3] GOULD V.: Semigroup of left quotients - the uniqueness problem. Proc. Edinburgh Math. Soc. (2) 35 (1992), 213-226. · Zbl 0791.20071
[4] JOHNSON R. E.: The extended centralizer of a ring over a module. Proc. Amer. Math. Soc. 2 (1951), 891-895. · Zbl 0044.02204
[5] LAMBEK J.: Lectures on Rings and Modules. Blaisdell Publ. Co., Waltham-Toronto-London, 1966. · Zbl 0143.26403
[6] UTUMI Y.: On quotient rings. Osaka J. Math. 8 (1956), 1-18. · Zbl 0070.26601
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