Methods In Ring Theory
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Author | : Vesselin Drensky |
Publisher | : CRC Press |
Total Pages | : 328 |
Release | : 2021-02-28 |
Genre | : Mathematics |
ISBN | : 1000657353 |
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"Furnishes important research papers and results on group algebras and PI-algebras presented recently at the Conference on Methods in Ring Theory held in Levico Terme, Italy-familiarizing researchers with the latest topics, techniques, and methodologies encompassing contemporary algebra."
Author | : Vesselin Drensky |
Publisher | : CRC Press |
Total Pages | : 332 |
Release | : 1998-03-27 |
Genre | : Mathematics |
ISBN | : 9780824701833 |
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"Furnishes important research papers and results on group algebras and PI-algebras presented recently at the Conference on Methods in Ring Theory held in Levico Terme, Italy-familiarizing researchers with the latest topics, techniques, and methodologies encompassing contemporary algebra."
Author | : B. Stenström |
Publisher | : Springer Science & Business Media |
Total Pages | : 319 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642660665 |
Download Rings of Quotients Book in PDF, Epub and Kindle
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 | : Freddy Van Oystaeyen |
Publisher | : Springer Science & Business Media |
Total Pages | : 569 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400963696 |
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Proceedings of the NATO Advanced Study Institute, Antwerp, Belgium, August 2-12, 1983
Author | : Constantin Nastasescu |
Publisher | : Springer Science & Business Media |
Total Pages | : 324 |
Release | : 2004-02-19 |
Genre | : Mathematics |
ISBN | : 9783540207467 |
Download Methods of Graded Rings Book in PDF, Epub and Kindle
The Category of Graded Rings.- The Category of Graded Modules.- Modules over Stronly Graded Rings.- Graded Clifford Theory.- Internal Homogenization.- External Homogenization.- Smash Products.- Localization of Graded Rings.- Application to Gradability.- Appendix A:Some Category Theory.- Appendix B: Dimensions in an abelian Category.- Bibliography.- Index.-
Author | : Bo Stenström |
Publisher | : |
Total Pages | : 0 |
Release | : 1975 |
Genre | : |
ISBN | : |
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Author | : Huishi Li |
Publisher | : World Scientific |
Total Pages | : 295 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 9814365149 |
Download Grobner Bases in Ring Theory Book in PDF, Epub and Kindle
1. Preliminaries. 1.1. Presenting algebras by relations. 1.2. S-graded algebras and modules. 1.3. [symbol]-filtered algebras and modules -- 2. The [symbol]-leading homogeneous algebra A[symbol]. 2.1. Recognizing A via G[symbol](A): part 1. 2.2. Recognizing A via G[symbol](A): part 2. 2.3. The [symbol-graded isomorphism A[symbol](A). 2.4. Recognizing A via A[symbol] -- 3. Grobner bases: conception and construction. 3.1. Monomial ordering and admissible system. 3.2. Division algorithm and Grobner basis. 3.3. Grobner bases and normal elements. 3.4. Grobner bases w.r.t. skew multiplicative K-bases. 3.5. Grobner bases in K[symbol] and KQ. 3.6. (De)homogenized Grobner bases. 3.7. dh-closed homogeneous Grobner bases -- 4. Grobner basis theory meets PBW theory. 4.1. [symbol]-standard basis [symbol]-PBW isomorphism. 4.2. Realizing [symbol]-PBW isomorphism by Grobner basis. 4.3. Classical PBW K-bases vs Grobner bases. 4.4. Solvable polynomial algebras revisited -- 5. Using A[symbol] in terms of Grobner bases. 5.1. The working strategy. 5.2. Ufnarovski graph. 5.3. Determination of Gelfand-Kirillov Dimension. 5.4. Recognizing Noetherianity. 5.5. Recognizing (semi- )primeness and PI-property. 5.6. Anick's resolution over monomial algebras. 5.7. Recognizing finiteness of global dimension. 5.8. Determination of Hilbert series -- 6. Recognizing (non- )homogeneous p-Koszulity via A[symbol]. 6.1. (Non- )homogeneous p-Koszul algebras. 6.2. Anick's resolution and homogeneous p-Koszulity. 6.3. Working in terms of Grobner bases -- 7. A study of Rees algebra by Grobner bases. 7.1. Defining [symbol] by [symbol]. 7.2. Defining [symbol] by [symbol]. 7.3. Recognizing structural properties of [symbol] via [symbol]. 7.4. An application to regular central extensions. 7.5. Algebras defined by dh-closed homogeneous Grobner bases -- 8. Looking for more Grobner bases. 8.1. Lifting (finite) Grobner bases from O[symbol]. 8.2. Lifting (finite) Grobner bases from a class of algebras. 8.3. New examples of Grobner basis theory. 8.4. Skew 2-nomial algebras. 8.5. Almost skew 2-nomial algebras
Author | : Ofer Gabber |
Publisher | : Springer Science & Business Media |
Total Pages | : 324 |
Release | : 2003 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 9783540405948 |
Download Almost Ring Theory Book in PDF, Epub and Kindle
Author | : Freddy Van Oystaeyen |
Publisher | : |
Total Pages | : 588 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9789400963702 |
Download Methods in Ring Theory Book in PDF, Epub and Kindle
Author | : Bo Stenström |
Publisher | : |
Total Pages | : |
Release | : 1975 |
Genre | : |
ISBN | : |
Download Rings of quotients Book in PDF, Epub and Kindle