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Tuesday, May 5, 2020 | History

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

Injective modules and injective quotient rings

by Carl Clifton Faith

  • 150 Want to read
  • 24 Currently reading

Published by M. Dekker in New York .
Written in English

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

  • Edition Notes

    Includes bibliographical references and index.

    StatementCarl Faith.
    SeriesLecture notes in pure and applied mathematics ;, v. 72
    Classifications
    LC ClassificationsQA251.3 .F34
    The Physical Object
    Paginationviii, 105 p. ;
    Number of Pages105
    ID Numbers
    Open LibraryOL4271318M
    ISBN 100824716329
    LC Control Number81017495

    Note. If Ris not a PID then a quotient of an injective R-module need not be injective. Note. If 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. C. Faith, Injective Modules and Injective Quotient Rings, Lecture Note in Pure and applied Math. 72 (Marcel Dekker,). Google ScholarAuthor: Kanzo Masaike.

    The general notion of injective objects is in section , the case of injective complexes in section Baer’s criterion is discussed in many texts, for example. N. Jacobsen, Basic Algebra II, W.H. Freeman and Company, See also. T.-Y. Lam, Lectures on modules and rings, Graduate Texts in Mathematics , Springer Verlag ( There is no analogous technique for injective modules, thus projective modules are, by and large, more important than injective modules. Consider the tensor product A×B. A is a quotient ring, R mod its second component J. Thus A×B is B/JB, or B/B, or 0. Thus A is not faithful. A ring homomorphism from R into S is faithful if S is a.

    INJECTIVE MODULES AND THE INJECTIVE HULL OF A MODULE, Novem MICHIEL KOSTERS Abstract. In the rst section we will de ne injective modules and we will prove some theorems. In the second section, we will de ne the concept of injective hull and show that any module has a ‘unique’ injective hull. We will follow [LA], section 3A and Size: KB. 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.


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

Injective Modules and Injective Quotient Rings (Lecture Notes Injective modules and injective quotient rings book Pure and Applied Mathematics) 1st Edition by Carl Faith (Author) 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: 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: $ *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis. ebook access is temporary and does not include ownership of the ebook.

Only valid for books with an ebook version. Springer Reference Works are not : Springer-Verlag Berlin Heidelberg. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Lectures on Injective Modules and Quotient Rings. 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 Faith. Pages Lectures on Injective Modules and Quotient Rings | Carl Faith | download | B–OK. Download books for free.

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

A ring is called hereditary if every quotient of an injective module is injective or, equivalently, if every submodule of a projective module is projective. We need a ring with a projective module with a nonprojective submodule. $\begingroup$ 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 R.

Injective quotient rings of commutative rings In book: Module Theory, pp A conjecture of the author dating to the middle s states that any FP2F ring R has FP-injective Author: Carl Faith. w-injective modules and w-semi-hereditary rings. we introduce the concept of w-injective modules and study some basic properties of w-injective modules.

and this book is the author's. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share.

RINGS WHOSE CYCLIC MODULES ARE INJECTIVE OR PROJECTIVE S. GOEL, S. JAIN AND SURJETT SINGH ABSTRACT. The object of this paper is to prove Theorem.

For a ring R the following are equivalent: (i) Every cyclic right R-module is injective or projective. (ii) R = S ffi T where S is semisimple artinian and T is a simple. A ring is right hereditary if and only if all its quotient modules by injective -modules are injective, and also if and only if the sum of two injective submodules of an arbitrary -module is injective.

If the ring is right hereditary and right Noetherian, then every -module contains a largest injective submodule. The projectivity (injectivity. Tags: group group theory homomorphism injective homomorphism kernel quotient quotient group representative Next story A Linear Transformation Maps the Zero Vector to the Zero Vector Previous story A Condition that a Commutator Group is a Normal Subgroup.

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].

Injective modules (Algebra) In the preface of this book, the authors express the view that 'a good working knowledge of injective modules is a sound investment for module theorists'. The existing literature on the subject has tended to deal with the applications of injective modules to ring theory.

] RINGS WHOSE QUASI-INJECTIVE MODULES ARE INJECTIVE Proof. Kaplansky has shown that a commutative ring is a V-ring if and only if it is regular. It is well known that a noetherian, regular ring is semisimple artinian.

Corollary. If Ris a V-ring then any artinian R-module is noetherian. SELF-INJECTIVE QUOTIENT RINGS AND INJECTIVE QUOTIENT MODULES 73 G5).

Therefore M is an injective i?-module. By theorem M is an injective Q module. Hence Q is semi-simple Artinian, see Cartan-Eilenberg [3, p Theorem ].

Conversely let Q be a semi-simple Artinian ring, then if M be a S-free and S-divisible i?-module, M can be regarded as a Q-module, the module com. Rings each of whose proper cyclic modules is injective Rings each of whose proper cyclic modules is injective Chapter: (p) 5 Rings each of whose proper cyclic modules is injective Source: Cyclic Modules and the Structure of Rings Author(s): S.

Jain Ashish K. Srivastava Askar A. Tuganbaev Publisher: Oxford University Press. An injective module over one ring, may not be injective over another, but there are well-understood methods of changing rings which handle special cases. Rings which are themselves injective modules have a number of interesting properties and include rings such as group rings of finite groups over fields.If C is injective, then q (D) = 0 for any quotient module D of C.

In particular, all cosyzygy modules in an injective resolution of a module are cotorsion-free. Proposition The following conditions are equivalent: a) q preserves monomorphisms, b) q is the zero functor, c) Author: Alex Martsinkovsky, Jeremy Russell.COTILTING VERSUS PURE-INJECTIVE MODULES FRANCESCA MANTESE, PAVEL RUZICKA, AND ALBERTO TONOLO Abstract.

Let R and S be arbitrary associative rings. A left R-module RW is said to be cotilting if the class of modules cogenerated by RW coincides with the class of left R-modules for which the func-tor Ext1 R (;W) vanishes.