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Author: K. R. Goodearl
Publisher:
ISBN: 9780821899229
Category : Associative rings
Languages : en
Pages : 88
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Book Description
Author: K. R. Goodearl
Publisher:
ISBN: 9780821899229
Category : Associative rings
Languages : en
Pages : 88
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Book Description
Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 0821818244
Category : Mathematics
Languages : en
Pages : 97
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Book Description
This paper is concerned with studying necessary and sufficient conditions on a ring [italic]R such that for certain classes of right [italic]R-modules, the singular submodule of any member of the class is a direct summand of the module. The classes of interest are the class of all right [italic]R-modules, the class of all finitely generated right [italic]R-modules, and the class of all right [italic]R-modules whose singular submodules have bounded order.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 226
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Author: M. J. Asensio
Publisher: Universidad Almería
ISBN: 9788482400136
Category : Mathematics
Languages : en
Pages : 236
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Book Description
Author: Surender K Jain
Publisher: World Scientific
ISBN: 9814553123
Category :
Languages : en
Pages : 394
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Book Description
This volume consists of a collection of invited papers on the theory of rings and modules, most of which were presented at the biennial Ohio State — Denison Conference, May 1992, in memory of Hans Zassenhaus. The topics of these papers represent many modern trends in Ring Theory. The wide variety of methodologies and techniques demonstrated will be valuable in particular to young researchers in the area. Covering a broad range, this book should appeal to a wide spectrum of researchers in algebra and number theory.
Author: J.H. Cozzens
Publisher: Springer
ISBN: 3540379835
Category : Mathematics
Languages : en
Pages : 221
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 264
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Author: Lance W. Small
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 552
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Author: B. Stenström
Publisher: Springer Science & Business Media
ISBN: 3642660665
Category : Mathematics
Languages : en
Pages : 319
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Book Description
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 resulting ring Q satisfies (i), with the extra requirement that SES, and (ii).
Author: Kenneth Goodearl
Publisher: CRC Press
ISBN: 9780824763541
Category : Mathematics
Languages : en
Pages : 224
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Book Description
