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Titlebook: Rings of Quotients; An Introduction to M Bo Stenstr?m Book 1975 Springer-Verlag Berlin Heidelberg 1975 Adjoint functor.Coproduct.Prime.Quot

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樓主
發(fā)表于 2025-3-21 17:45:21 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Rings of Quotients
副標題An Introduction to M
編輯Bo Stenstr?m
視頻videohttp://file.papertrans.cn/831/830424/830424.mp4
叢書名稱Grundlehren der mathematischen Wissenschaften
圖書封面Titlebook: Rings of Quotients; An Introduction to M Bo Stenstr?m Book 1975 Springer-Verlag Berlin Heidelberg 1975 Adjoint functor.Coproduct.Prime.Quot
描述The theory of rings of quotients has its origin in the work of (j). Ore and K. Asano on the construction of the total ring of fractions, in the 1930‘s and 40‘s. But the subject did not really develop until the end of the 1950‘s, when a number of important papers appeared (by R. E. Johnson, Y. Utumi, A. W. Goldie, P. Gabriel, J. Lambek, and others). Since then the progress has been rapid, and the subject has by now attained a stage of maturity, where it is possible to make a systematic account of it (which is the purpose of this book). The most immediate example of a ring of quotients is the field of fractions Q of a commutative integral domain A. It may be characterized by the two properties: (i) For every qEQ there exists a non-zero SEA such that qSEA. (ii) Q is the maximal over-ring of A satisfying condition (i). The well-known construction of Q can be immediately extended to the case when A is an arbitrary commutative ring and S is a multiplicatively closed set of non-zero-divisors of A. In that case one defines the ring of fractions Q = A [S-l] as consisting of pairs (a, s) with aEA and SES, with the declaration that (a, s)=(b, t) if there exists UES such that uta = usb. The re
出版日期Book 1975
關(guān)鍵詞Adjoint functor; Coproduct; Prime; Quotientenring; Rings; algebra; colimit
版次1
doihttps://doi.org/10.1007/978-3-642-66066-5
isbn_softcover978-3-642-66068-9
isbn_ebook978-3-642-66066-5Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 1975
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沙發(fā)
發(fā)表于 2025-3-21 21:12:51 | 只看該作者
Introduction,nd 40’s. But the subject did not really develop until the end of the 1950’s, when a number of important papers appeared (by R.E. Johnson, Y. Utumi, A. W. Goldie, P. Gabriel, J. Lambek, and others). Since then the progress has been rapid, and the subject has by now attained a stage of maturity, where
板凳
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地板
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5#
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6#
發(fā)表于 2025-3-22 16:32:16 | 只看該作者
Torsion Theory,we get to consider general rings of quotients of ., but here we will follow a converse course. We start by axiomatizing the concept of torsion, and then to each torsion theory we associate a ring of quotients. This chapter is devoted to a comprehensive study of the general aspects of torsion. The ba
7#
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8#
發(fā)表于 2025-3-22 21:34:46 | 只看該作者
Simple Torsion Theories,rings, for which all hereditary torsion theories are simple. Therefore it is of a certain interest to study simple torsion theories in some detail. The methods to be used for that purpose are the basic ones of the theory of artinian rings, such as the use of the Jacobson radical and the lifting of i
9#
發(fā)表于 2025-3-23 04:34:59 | 只看該作者
Rings and Modules of Quotients,ients . of a non-singular ring .. This was done before the theory of injective envelopes had become available, but it was later proved that . could be used as an injective envelope of the ring .. The maximal ring of quotients of an arbitrary ring . was defined by Utumi [1] and studied by Findlay and
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發(fā)表于 2025-3-23 06:44:19 | 只看該作者
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