Last edited by Grokasa
Tuesday, April 28, 2020 | History

6 edition of Lectures on injective modules and quotient rings found in the catalog.

Lectures on injective modules and quotient rings

Carl Clifton Faith

Lectures on injective modules and quotient rings

  • 179 Want to read
  • 23 Currently reading

Published by Springer-Verlag in Berlin, New York [etc.] .
Written in English

    Subjects:
  • Quotient rings.,
  • Injective modules (Algebra)

  • Edition Notes

    Bibliography: p. 132-137.

    Statementby Carl Faith.
    SeriesLecture notes in mathematics,, 49, Lecture notes in mathematics (Springer-Verlag) ;, 49.
    Classifications
    LC ClassificationsQA3 .L28 no. 49
    The Physical Object
    Paginationxv, 140 p.
    Number of Pages140
    ID Numbers
    Open LibraryOL5552066M
    LC Control Number67031680

    In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.A module over a ring is a generalization of the notion of vector space over a field, wherein the corresponding scalars are the elements of an arbitrary given ring (with identity) and a multiplication (on the left and/or on the right) is defined between elements of the ring and elements of the module. Generalization. More generally, let C be an abelian object E is an injective hull of an object M if M → E is an essential extension and E is an injective object.. If C is locally small, satisfies Grothendieck's axiom AB5 and has enough injectives, then every object in C has an injective hull (these three conditions are satisfied by the category of modules over a ring). Ring Theory and Its Applications: Ring Theory Session in Honor of T. Y. Lam on His 70th Birthday, 31st Ohio State-denison Mathematics Conference, May Ohio State Univer.


Share this book
You might also like
Homeward songs by the way

Homeward songs by the way

A New England boyhood

A New England boyhood

Some biological aspects of the Nolina smut fungus, Clintamra nolinae comb. nov.

Some biological aspects of the Nolina smut fungus, Clintamra nolinae comb. nov.

Professor

Professor

spirit of The Gregorian chant.

spirit of The Gregorian chant.

report on the problems of development facing the town of Stoney Creek.

report on the problems of development facing the town of Stoney Creek.

Memoirs of the Prince de Talleyrand.

Memoirs of the Prince de Talleyrand.

TAIT Office 2000 Premium Pack - Value Pack (old version)

TAIT Office 2000 Premium Pack - Value Pack (old version)

Historic gardens of Virginia

Historic gardens of Virginia

Grigorescu

Grigorescu

Image-beyond image

Image-beyond image

Life beyond time management

Life beyond time management

garden of delights

garden of delights

Annie E. Nolan.

Annie E. Nolan.

New England

New England

Staying power

Staying power

Lectures on injective modules and quotient rings by Carl Clifton Faith Download PDF EPUB FB2

Lectures on Injective Modules and Quotient Rings. Authors: Faith, Carl Free PreviewBrand: Springer-Verlag Berlin Heidelberg. Lectures on Injective Modules and Quotient Rings / Edition 1 available in Paperback.

Add to Wishlist. ISBN ISBN Pub. Date: 01/01/ Publisher: Springer Berlin Heidelberg. Lectures on Injective Modules and Quotient Rings / Edition 1. by Carl Faith in rings.- The endomorphism ring of a quasi-injective module Price: $ Injective Modules and Injective Quotient Rings (Lecture Notes in Pure and Applied Mathematics) 1st Edition by Carl Faith (Author) ISBN ISBN Lectures on injective modules and quotient rings book is ISBN important.

ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Cited by: Lectures on Injective Modules and Quotient Rings.

Lectures on injective modules and quotient rings book Authors; Carl Faith; Book. 99 Search within book. Front Matter. Pages I-XV. PDF. Injective modules. Carl Faith. Pages The endomorphism ring of a quasi-injective module. Carl Faith. Pages Noetherian, artinian, and semisimple modules and rings.

Carl Lectures on injective modules and quotient rings book. Pages Lectures on Injective Modules and Quotient Rings | Carl Faith | download | B–OK. Download books for free. Lectures on injective modules and quotient rings book Find books. Lectures on Rings and Modules Reprint Edition the classical structure theory of associative rings, injective modules, and rings of quotients.

The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Cited by: Lectures on injective modules and quotient rings.

Berlin, New York [etc.] Springer-Verlag, (OCoLC) Material Type: Internet Lectures on injective modules and quotient rings book Document Type: Book, Internet Resource: All Authors / Contributors: Carl Faith.

Get this from a library. Lectures on injective modules and quotient rings. [Carl Faith]. Lectures on Modules and Rings (Graduate Texts in Mathematics) th Edition by Tsit-Yuen Lam (Author) out of 5 stars 3 ratings.

ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book.

Cited by: These are the rings in which every module is injective. This follows from this existence of injective envelopes. This is often proven using an injective producing lemma (as in this excerpt from Lam's Modules and Rings). Lam's textbook contains many examples of injective modules on surrounding pages.

The focus of this book is the study of the noncommutative aspects of rings and modules, and the style will make it accessible to anyone with a background in basic abstract algebra. When compared to other more encyclopedic texts, the sharp focus of this book accommodates students meeting this material for the first by: Lectures on injective modules and quotient rings.

Berlin, New York [etc.] Springer-Verlag, (DLC) (OCoLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Carl Faith.

Lectures on Modules and Rings. Authors: Lam, Tsit-Yuen Free Preview. Buy this book eB99 Projective, and Injective Modules. Pages Book Title Lectures on Modules and Rings Authors. Tsit-Yuen Lam; Series Title Graduate Texts in Brand: Springer-Verlag New York. This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students.

The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained.

Lectures on Modules and Rings. Tsit-Yuen Lam. Springer Science & Business Media, - Mathematics - pages. 0 Reviews. Textbook writing must be one of the cruelest of self-inflicted tortures. Cite this chapter as: Faith C.

() Injective modules. In: Lectures on Injective Modules and Quotient Rings. Lecture Notes in Mathematics, vol This set of lecture notes is focused on the noncommutative aspects of the study of rings and modules.

It is intended to complement the book Steps in Commutative Algebra, by R. Sharp, which provides excellent coverage of the commutative theory. Faith C. () Noetherian, artinian, and semisimple modules and rings.

In: Lectures on Injective Modules and Quotient Rings. Lecture Notes in Mathematics, vol Author: Carl Faith. $\begingroup$ I am not really sure I understand what you are asking for: Is there possibly a mix up between modules and rings. More precisely, do you actually want to consider R (the direct product of fields) as a ring.

The most natural question along the lines of your question to me would be: for some ring R find an injective R-module M such that a quotient module M/N is not an injective. Publisher of Humanities, Social Science & STEM Books Skip to main content.

Free Standard Shipping. Injective Modules and Injective Quotient Rings By Faith. Paperback $ eBook $ ISBN Published Janu by CRC Press Pages. Cite this chapter as: Faith C. () Quasi-Injective modules.

In: Lectures on Injective Modules and Quotient Rings. Lecture Notes in Mathematics, vol Author: Carl Faith. Cite this chapter as: Faith C. () Maximal quotient rings. In: Lectures on Injective Modules and Quotient Rings.

Lecture Notes in Mathematics, vol Cited by: 9. An outgrowth of the author’s lecture courses and seminars over the years at the University of California at Berkeley, this book and its predecessor Exercises in Classical Ring Theory (Springer, ) offer to the mathematics community the fullest and most comprehensive reference to date for problem solving in the theory of modules and by: First published in These lectures are in two parts.

Part I, entitled injective Modules Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E,R) of right ideals annihilated by subsets of E.

Part II is on the subject of (F)PF, or (finitely) pseudo-Frobenius, rings [i.e., all (finitely generated) faithful modules generate the category mod-R of all R-modules].

Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange. Download books "Mathematics - Lectures". Ebook library | B–OK.

Download books for free. Find books. Injective Modules and Injective Quotient Rings - CRC Press Book Injective Modules and Injective Quotient Rings 1st Edition.

Faith. Paperback $ eBook $ eBook Rental Published Janu Reference - Pages ISBN - CAT# DK Series: Lecture Notes in Pure and Applied Mathematics For Instructors. rich module theory over non-associative rings A. For this, Ais considered as module over the (associative) multiplication algebra M(A) and the category σ[A] is investigated.

Also torsion modules over a topological ring and graded modules over a graded ring. The idea of writing this book came roughly at the time of publication of my graduate text Lectures on Modules and Rings, Springer GTM Vol.Since that time, teaching obligations and intermittent intervention of other projects caused prolonged delays in the work on this volume.

Only a lucky break in my schedule in enabled me to put the 5/5(1). Author of Algebra: rings, modules and categories, Algebra, Rings And Things And A Fine Array Of Twentieth Century Associative Algebra (Mathematical Surveys and Monographs), Classification of commutative FPF rings, FPF ring theory, Algebra II, Lectures on injective modules and quotient rings, Lectures on injective modules and quotient rings.

Books •There is a long list of recommended books in the schedules. •J.B. raleigh,F A First Course in Abstract Algebra •B. Hartley, T.O. Hawkes, Rings, Modules and Linear Algebra •.J.P Cameron, Intrductiono to Algebra •M.

Artin, Algebra cturLee 1. In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free s equivalent characterizations of these modules appear below.

Every free module is a projective module, but the converse fails to hold over some rings, such as Dedekind rings. Recall the following characterization of indecomposable injective modules. Lemma. If M is an injective module over a commutative noetherian ring R, the following conditions are equivalent: (1) M is indecomposable.

(2) M is the injective envelope of every non-trivial submodule. (3) The zero submodule is irreducible in Size: KB. Definition. A left module Q over the ring R is injective if it satisfies one (and therefore all) of the following equivalent conditions.

If Q is a submodule of some other left R-module M, then there exists another submodule K of M such that M is the internal direct sum of Q and K, i.e.

Q + K = M and Q ∩ K = {0}.; Any short exact sequence 0 →Q → M → K → 0 of left R-modules splits. A module M is called simple if the only submodules of M are 0 and M. For example, Cn is a simple Mn(C){module because given any nonzero vector, you can flnd a matrix which takes it to any other nonzero vector.

Every module can be built up out of simple modules in the following sense Deflnition Let M be a Size: KB. A submodule of an injective module need not be injective.

The first example that comes to mind is $\Bbb Z$ as a submodule of $\Bbb Q$ (as $\Bbb Z$ modules). A quotient of a divisible module is divisible (you can simply push through the quotient map).

Thus, any counterexample cannot be over a ring where divisible $\Rightarrow$ injective. T.-Y. Lam, Lectures on modules and rings, Graduate Texts in MathematicsSpringer Verlag (). Section of. Peter May, Notes on Tor and Ext ; For abelian sheaves over the etale site: James Milne, section 8 of Lectures on Étale Cohomology; A study of injective modules in higher algebra: Liran Shaul, Injective DG-modules over non.

Basic module theory Octo 1 Basic de nitions Let Rbe a ring, which will often be assumed to have an identity 1. De nition A left R-module is an abelian group Mand an \external law of composition"File Size: KB. Chapter II. Structured ring and module spectra 35 1.

The category of S-modules 35 2. The mirror image to the category of S-modules 39 3. S-algebras and their modules 41 4. Free A∞ and E∞ ring spectra and comparisons of definitions 44 5.

Free modules over A∞ and E∞ ring spectra 47 6. Composites of monads and monadic tensor products 50 Size: 1MB. injective), if is SS- -injective (r esp. SS- -injective for every right -module). Some characterizations and properties of (strongly) SS-injective modules and rings are given.

In ring theory, a branch pdf abstract algebra, a quotient ring, also known as factor pdf, difference ring or residue class ring, is a construction quite similar to the quotient groups of group theory and the quotient spaces of linear algebra. It is a specific example of a quotient, as viewed from the general setting of universal starts with a ring R and a two-sided ideal I in R.Note.

If Ris not a PID then a quotient of an injective R-module need not be injective. Note. Download pdf Ris a ring with identity then for any R-module M there exists an epimorphism of R-modules: f: P! M where Pis a projective module (take e.g.

P= L m2M R). Theorem. If Ris a ring with identity then for any R-module M there exist a File Size: KB.(ii) Ebook ring isomorphism is a bijective ring homomorphism.

(iii) The rings Rand Sare called isomorphic if there exists a ring ebook ’: R!S. Example 1: Let R= Z and I= nZ for some n>1. Let us show that the quotient ring R=I= Z=nZ is isomorphic to Z n (as a ring). Proof. In the course of our study of quotient groups we have already seen thatFile Size: KB.