Buy Dimensions of Ring Theory by Freddy Van Oystaeyen
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Home > Mathematics and Science Textbooks > Mathematics > Algebra > Dimensions of Ring Theory: (36 Mathematics and Its Applications)
36%
Dimensions of Ring Theory: (36 Mathematics and Its Applications)

Dimensions of Ring Theory: (36 Mathematics and Its Applications)


     0     
5
4
3
2
1



Available


X
About the Book

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of s9phistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non- trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Table of Contents:
1. Finiteness Conditions for Lattices.- 1.1. Lattices.- 1.2. Noetherian and Artinian Lattices.- 1.3. Lattices of Finite Length.- 1.4. Irreducible Elements in a Lattice.- 1.5. Goldie Dimension of a Modular Lattice.- 1.6. Goldie Dimension and Chain Conditions for Modular Lattices with Finite Group Actions.- 1.7. Complements and Pseudo-Complements.- 1.8. Semiatomic Lattices and Compactly Generated Lattices.- 1.9. Semiartinian Lattices.- 1.10. Indecomposable Elements in a Lattice.- 1.11. Exercises.- Bibliographical Comments to Chapter 1.- 2. Finiteness Conditions for Modules.- 2.1. Modules.- 2.2. The Lattice of Submodules of a Module.- 2.3. Noetherian and Artinian Modules.- 2.4. Modules of Finite Length.- 2.5. Semisimple Modules.- 2.6. Semisimple and Simple Artinian Rings.- 2.7. The Jacobson Radical and the Prime Radical of a Ring.- 2.8. Rings of Fractions. Goldie’s Theorems.- 2.9. Artinian Modules which are Noetherian.- 2.10. Projective and Infective Modules.- 2.11. Tensor Product and Flat Modules.- 2.12. Normalizing Extensions of a Ring.- 2.13. Graded Rings and Modules.- 2.14. Graded Rings and Modules of Type ?. Internal Homogenisation.- 2.15. Noetherian Modules over Graded Rings of Type ?. Applications.- 2.16. Strongly Graded Rings and Clifford Systems for Finite Groups.- 2.17. Invariants of a Finite Group Action.- 2.18. Exercises.- Bibliographical Comments to Chapter 2.- 3. Krull Dimension and Gabriel Dimension of an Ordered Set.- 3.1. Definitions and Basic Properties.- 3.2. The Krull Dimension of a Modular Lattice.- 3.3. Critical Composition Series of a Lattice.- 3.4. The Gabriel Dimension of a Modular Lattice.- 3.5. Comparison of Krull and Gabriel Dimension.- 3.6. Exercises.- Bibliographical Comments to Chapter 3.- 4. Krull Dimension and Gabriel Dimension ofRings and Modules.- 4.1. Definitions and Generalities.- 4.2. Krull and Gabriel Dimension of Some Special Classes of Rings and Modules.- 4.3. Exercises.- Bibliographical Comments to Chapter 4.- 5. Rings with Krull Dimension.- 5.1. Nil Ideals.- 5.2. Semiprime Rings with Krull Dimension.- 5.3. Classical Krull Dimension of a Ring.- 5.4. Associated prime Ideals.- 5.5. Fully Left Bounded Rings with Krull Dimension.- 5.6. Examples of Noetherian Rings of Arbitrary Krull Dimension.- 5.7. Exercises.- Bibliographical Comments to Chapter 5.- 6. Krull Dimension of Noetherian Rings. The Principal Ideal Theorem.- 6.1. Fully Left Bounded Left Noetherian Rings.- 6.2. The Reduced Rank of a Module.- 6.3. Noetherian Rings Satisfying Condition H.- 6.4. Fully Bounded Noetherian Rings.- 6.5. Krull Dimension and Invertible Ideals in a Noetherian Ring.- 6.6. The Principal Ideal Theorem.- 6.7. Exercises.- Bibliographical Comments to Chapter 6.- 7. Relative Krull and Gabriel Dimensions.- 7.1. Additive Topologies and Torsion Theories.- 7.2. The Lattices CF (M) and CHg.- 7.3. Relative Krull Dimension.- 7.4. Relative Krull Dimension Applied to the Principal Ideal Theorem.- 7.5. Relative Gabriel Dimension.- 7.6. Relative Krull and Gabriel Dimensions of Graded Rings.- 7.7. Exercises.- Bibliographical Comments to Chapter 7.- 8. Homological Dimensions.- 8.1. The Projective Dimension of a Module.- 8.2. Homological Dimension of Polynomial Rings and Rings of Formal Power Series.- 8.3. Injective Dimension of a Module.- 8.4. The Flat Dimension of a Module.- 8.5. The Artin-Rees Property and Homological Dimensions.- 8.6. Regular Local Rings.- 8.7. Exercises.- Bibliographical Comments to Chapter 8.- 9. Rings of Finite Global Dimension.- 9.1. The Zariski Topology.- 9.2. The Local Study of Homological Dimension.- 9.3. Rings Integral over their Centres.- 9.4. Commutative Rings of Finite Global Dimension.- 9.5. Exercises.- Bibliographical Comments to Chapter 9.- 10. The Gelfand-Kirillov Dimension.- 10.1. Definitions and Basic Properties.- 10.2. GK-dimension of Filtered and Graded Algebras.- 10.3. Applications to Special Classes of Rings.- 10.4. Exercises.- Bibliographical Comments to Chapter 10.- References.


Best Sellers


Product Details
  • ISBN-13: 9789401082075
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Height: 235 mm
  • No of Pages: 360
  • Returnable: N
  • Width: 155 mm
  • ISBN-10: 9401082073
  • Publisher Date: 07 Oct 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: 36 Mathematics and Its Applications


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Dimensions of Ring Theory: (36 Mathematics and Its Applications)
Springer -
Dimensions of Ring Theory: (36 Mathematics and Its Applications)
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Dimensions of Ring Theory: (36 Mathematics and Its Applications)

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!