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ISPC Materials and technologies, Philadelphia, USA |
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* Scientific Article * Impact Factor 6.630 |
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Mushrub VA, Sukhorukova IV, Mochalina EP, Ivankova GV
ON F-PRIME RINGS AND THEIR F-RINGS OF QUOTIENTS. |
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Full Article: PDF
Scientific Object Identifier: http://s-o-i.org/1.1/TAS-07-51-18
DOI: https://dx.doi.org/10.15863/TAS.2017.07.51.18
Language: English
Citation: Mushrub VA, Sukhorukova IV, Mochalina EP, Ivankova GV (2017) ON F-PRIME RINGS AND THEIR F-RINGS OF QUOTIENTS. ISJ Theoretical & Applied Science, 07 (51): 107-110. Soi: http://s-o-i.org/1.1/TAS-07-51-18 Doi: https://dx.doi.org/10.15863/TAS.2017.07.51.18 |
Pages: 107-110
Published: 30.07.2017
Abstract: All rings are associative in what follows. We will also assume that all rings are unital and all ring homomorphisms preserve the identity. Throughout the paper, B stands for a unitary associative ring and f is an automorphism of B. The main purpose of the work is to describe the left f-ring of quotients Q_f (B) of B. Our methods is not connected with right flat epimorphic hull, but we use a fruitful construction based on a direct limit to build the f-ring of quotients. The principal results to be given are Theorems 1 and 2 below. Theorem 1 establishes that Q_f (B) is embeddable in the complete left ring of quotients Q_max (B) and the ring B is a subring of Q_f (B). Theorem 2 asserts that the centres of the left and right f-ring of quotients rings coincides. The authors have intention to continue this study in their subsequent articles. Therefore, at the end of the paper, we formulate a hypothesis, for the proof of which we need the results of this work.
Key words: associative rings; f-rings of quotients; f-prime rings.
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