Home > Mathematics and Science Textbooks > Mathematics > Algebra > A Course in Constructive Algebra: (Universitext)
37%
A Course in Constructive Algebra: (Universitext)

A Course in Constructive Algebra: (Universitext)

          
5
4
3
2
1

Available


Premium quality
Premium quality
Bookswagon upholds the quality by delivering untarnished books. Quality, services and satisfaction are everything for us!
Easy Return
Easy return
Not satisfied with this product! Keep it in original condition and packaging to avail easy return policy.
Certified product
Certified product
First impression is the last impression! Address the book’s certification page, ISBN, publisher’s name, copyright page and print quality.
Secure Checkout
Secure checkout
Security at its finest! Login, browse, purchase and pay, every step is safe and secured.
Money back guarantee
Money-back guarantee:
It’s all about customers! For any kind of bad experience with the product, get your actual amount back after returning the product.
On time delivery
On-time delivery
At your doorstep on time! Get this book delivered without any delay.
Quantity:
Add to Wishlist

About the Book

The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr"uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit; much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc­ tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden'of analysis rather than a theory of discrete algebraic structures.

Table of Contents:
I. Sets.- 1. Constructive vs. classical mathematics.- 2. Sets, subsets and functions.- 3. Choice.- 4. Categories.- 5. Partially ordered sets and lattices.- 6. Well-founded sets and ordinals.- II. Basic Algebra.- 1. Groups.- 2. Rings and fields.- 3. Real numbers.- 4. Modules.- 5. Polynomial rings.- 6. Matrices and vector spaces.- 7. Determinants.- 8. Symmetric polynomials.- III. Rings And Modules.- 1. Quasi-regular ideals.- 2. Coherent and Noetherian modules.- 3. Localization.- 4. Tensor products.- 5. Flat modules.- 6. Local rings.- 7. Commutative local rings.- IV. Divisibility in Discrete Domains.- 1. Cancellation monoids.- 2. UFD's and Bézout domains.- 3. Dedekind-Hasse rings and Euclidean domains.- 4. Polynomial rings.- V. Principal Ideal Domains.- 1. Diagonalizing matrices.- 2. Finitely presented modules.- 3. Torsion modules, p-components, elementary divisors.- 4. Linear transformations.- VI. Field Theory.- 1. Integral extensions and impotent rings.- 2. Algebraic independence and transcendence bases.- 3. Splitting fields and algebraic closures.- 4. Separability and diagonalizability.- 5. Primitive elements.- 6. Separability and characteristic p.- 7. Perfect fields.- 8. Galois theory.- VII. Factoring Polynomials.- 1. Factorial and separably factorial fields.- 2. Extensions of (separably) factorial fields.- 3. Condition p.- 4. The fundamental theorem of algebra.- VIII. Commutative Noetherian Rings.- 1. The Hilbert basis theorem.- 2. Noether normalization and the Artin-Rees lemma.- 3. The Nullstellensatz.- 4. Tennenbaum' s approach to the Hilbert basis theorem.- 5. Primary ideals.- 6. Localization.- 7. Primary decomposition.- 8. Lasker-Noether rings.- 9. Fully Lasker-Noether rings.- 10. The principal ideal theorem.- IX. Finite Dimensional Algebras.- 1. Representations.- 2. The density theorem.- 3. The radical and summands.- 4. Wedderburn's theorem, part one.- 5. Matrix rings and division algebras.- X. Free Groups.- 1. Existence and uniqueness.- 2. Nielsen sets.- 3.Finitely generated subgroups.- 4. Detachable subgroups of finite-rank free groups.- 5. Conjugate subgroups.- XI. Abelian Groups.- 1. Finite-rank torsion-free groups.- 2. Divisible groups.- 3. Height functions on p-groups.- 4. Ulm's theorem.- 5. Construction of Ulm groups.- XII. Valuation Theory.- 1. Valuations.- 2. Locally precompact valuations.- 3. Pseudofactorial fields.- 4. Normed vector spaces.- 5. Real and complex fields.- 6. Hensel's lemma.- 7. Extensions of valuations.- 8. e and f.- XIII. Dedekind Domains.- 1. Dedekind sets of valuations.- 2. Ideal theory.- 3. Finite extensions.


Best Sellers


Product Details
  • ISBN-13: 9780387966403
  • Publisher: Springer-Verlag New York Inc.
  • Publisher Imprint: Springer-Verlag New York Inc.
  • Height: 235 mm
  • No of Pages: 344
  • Returnable: Y
  • Spine Width: 19 mm
  • Width: 155 mm
  • ISBN-10: 0387966404
  • Publisher Date: 18 Dec 1987
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: Universitext
  • Weight: 503 gr


Similar Products

How would you rate your experience shopping for books on Bookswagon?

Add Photo
Add Photo

Customer Reviews

REVIEWS           
Click Here To Be The First to Review this Product
A Course in Constructive Algebra: (Universitext)
Springer-Verlag New York Inc. -
A Course in Constructive Algebra: (Universitext)
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.

A Course in Constructive Algebra: (Universitext)

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

    New Arrivals


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!
    ASK VIDYA