Perfect torsion theories and Morita contexts

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Torsion theory (Alg
Statementby Michael Whitney Rennie.
The Physical Object
Paginationvi, 50 l.
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Open LibraryOL16745503M

Results in the literature are special cases or follow immediately [12, 15, 23, 38]. Consider first an arbitrary hereditary torsion theory on mod R, and the TlIIi; QUOTIENT CATEGORY OF A MORITA CONTEXT lattice of submodules of a fixed -R-module X.

A submodule A is called closed if XjA e g- (A e C^(X) in [39, p. 58]).Cited by:   A Morita-Takeuchi context (C,D,cMD,oNc,f,g) consists of coalge- bras C and D, bicomodules cMo and oNc, and bicolinear maps /: C MOoN and F.C.

Iglesias, J.G. Torrecillas 1 Journal of Pure and Applied Algebra () g: D NOcM making the following diagrams commute: MMDpD NNQcC \8 \IDf CDc^-^^^Dfl^Dc^ fl^-^-^^Dc^DD^ Let us fix a Cited by:   There have been a number of papers relating the rings R and S of a Morita context.

For instance, Mueller [14] examined the relationship between torsion theories over R and S. Also Cohen [5] has used Morita contexts to obtain information about the relationship between a ring R and its fixed ring R0, where G is a finite group of automorphisms of by: 4. If (sé, 38) is a torsion theory with idempotent radical T, then (sé, 38) is hereditary if and only if F is a left exact functor [7, Propositionp.

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(In this context if f:M-+N, then T(f) is the restriction off to T(M).) 2. Cohereditary torsion theories. Theorem If (sé, 38) is a perfect torsion theory, then (sé, 38) is. Perfect projectors In this section we apply the results of section 2 and some results concerning torsion theories to give a number of characterizations of perfect projectors over semi perfect rings.

A ring R is called semi-perfect if each cyclic left R-module has a projective by: 4. Let T denote the Morita Context (A, B, V, W, ψ, φ) as defined in Section 1. Chen [6, Theorem 4] also showed that if A and B have many full elements, so does T. A.I. Kashu, Morita contexts and the correspondences between the lattices of submodules, Bull.

Academy Sci. Moldova, Math. 1 (14) () (in Russian). [4] A.I. Kashu, Torsion theories and dualities in a Morita context. Perfect Gabriel filters of right ideals and their corresponding right rings of quotients have the desirable feature that every module of quotients is determined solely by the right ring of We also demonstrate that Morita's construction of can be adapted to the construction of.

Keywords: Torsion theory Topics in Torsion Theory, Math. This constitutes much of Chapter 4 -the Morita theorem is Theorem 4. and the basis for it is a corre­ spondence theorem for projective modules (Theorem 4. 7) suggested by the Morita context. As a by-product, this provides foundation for a rather complete theory of simple Noetherian rings-but more about this in the introduction.

hereditary faithful torsion theory. The Gabriel filter of this torsion theory is the set of Perfect torsion theories and Morita contexts book dense right ideals (see Proposition VIp. in [20]).

Description Perfect torsion theories and Morita contexts PDF

(2) The class of nonsingular modules over a ring R is closed under submodules, extensions, products and injective envelopes.

Thus, it is a torsion-free class of a hereditary torsion theory. tively Hermitian Morita Theory, is called a torsion triple, if which includes some partial version of the Morita theorems in the hermitian context. As we will show in this note, the.

This paper contains a long summary of the basic properties of higher FR torsion. An attempt is made to simplify the constructions from my book Higher Franz-Reidemeister Torsion (IP/AMS Studies in Advanced Math 31).

Some new basic theorems are also proved such as the Framing Principle in full generality. This is used to compute the higher torsion for bundles with closed even dimensional.

We prove that every perfect torsion theory for a ring R is differential (in the sense of [P.E. Bland, Differential torsion theory, Journal of Pure and Applied Algebra () 1–8]). A Morita theory is developed in [6] for nonunital rings in the case where the equivalence is given by a tensor functor.

It is also proved there that equivalences between categories of firm modules. The papers of this volume share as a common goal the structure and classi- fication of noncommutative rings and their modules, and deal with topics of current research including: localization, serial rings, perfect endomorphism rings, quantum groups, Morita contexts, generalizations of.

In this paper, we show that if rings A and B are (s, 2)-rings, then so is the ring of a Morita context (A, B, M, N,). Also we get analogous results for unit 1-stable ranges and GM-rings.

These differences are all torsion phenomena, and rationally there is no difference between algebraic and topological triangulated categories.

A triangulated category is algebraic in the sense of Keller [Ke, ] if it is triangle equivalent to the stable category of a Frobenius category, i.e., an exact category with enough injectives and enough. This constitutes much of Chapter 4 -the Morita theorem is Theorem 4. and the basis for it is a correƯ spondence theorem for projective modules (Theorem 4.

7) suggested by the Morita context. As a by-product, this provides foundation for a rather complete theory of simple Noetherian rings-but more about this in the introduction.

Auxiliary Results on Commutative Localization.- 6. The Topologies?Mn for a Commutative Noetherian Ring.- Exercises.- VIII. Simple Torsion Theories.- 1. The Jacobson Radical and Artinian Rings.- 2.

Semi-Artinian Modules and Rings.- 3. Simple Torsion Theories.- 4. Semi-Perfect Rings.- 5. Perfect Rings.- 6. Hereditary Torsion Theories for a. We consider a generalization of the notion of torsion theory, which is associated with a Serre subcategory over a commutative Noetherian ring.

In Aghapournahr and Melkersson investigated the question of when local cohomology modules belong to a Serre subcategory of the module category. In their study, the notion of Melkersson condition was defined as a suitable condition.

On Commutativity of 2-torsion free *-prime Rings with Generalized Derivations, Mathematica cluj, (76)(1) (December ). Lie ideals and jordan triple derivations in rings, Rendiconti del Seminario Matematico della Università di Padova, (), namely localisation of spectra with respect to a homology theory and A-torsion R-modules where A is a perfect algebra over the commutative ring R.

In Section 2 we recall some definitions in the context of model categories, namely sta-bility, framings, properness and cofibrant generation. These technical definitions will play. Abstract: We study left and right Bousfield localisations of stable model categories which preserve stability.

This follows the lead of the two key examples: localisations of spectra with respect to a homology theory and A-torsion modules over a ring R with A a perfect R-algebra. A mathematical formulation in terms of torsion-full first-order integrable G-structures on supermanifolds (for low dimensional supergravity theories) is given in.

John Lott, The Geometry of Supergravity Torsion Constraints Comm. Math. Phys. (), –, (exposition in arXiv) which is followed up in.

Torsion or twisting is a common concept in mechanical engineering systems. This section looks at the basic theory associated with torsion and examines some typical examples by calculating the main parameters.

The papers of this volume share as a common goal the structure and classi- fication of noncommutative rings and their modules, and deal with topics of current research including: localization, serial rings, perfect endomorphism rings, quantum groups, Morita contexts, generalizations of.

The purpose of this book is to provide the reader with a quick introduction to torsion theory and to study selected properties of rings and modules in this setting. The material presented ranges from a torsion theoretical treatment of standard topics in ring and module theory to how previously untreated properties of rings and modules might be Author: Paul E.

Bland. Torsion formula. The torsional shear stress can be calculated using the following formula: Note: T is the internal torque at the region of interest, as a result of external torque loadings applied to the member (units: Nm) ; r is the radius of the point where we are calculating the shear stress (units: m or mm) ; J is the polar moment of inertia for the cross-section (units: m 4 or mm 4).

examples, namely localisation of spectra with respect to a homology theory and A-torsion R-modules where A is a perfect complex over the commutative ring R.

In Section 3, we recall some definitions in the context of model categories, namely stability, framings, properness and cofibrant generation. These technical definitions. The most natural and general context to define the torsion would involve recent introductory book [] by V. Turaev are excellent sources to fill in many of Chapter 4 discusses more analytic descriptions of the Reidemeister torsion: in terms of gauge theory, in terms of Morse theory, and in terms of Hodge theory.

We. ISBN: OCLC Number: Language Note: English. Description: 1 online resource: Contents: Kasch Modules --Compactness in Categories and Interpretations --A Ring of Morita Context in Which Each Right Ideal is Weakly Self-injective --Splitting Theorems and a Problem of Müller --Decompositions of D1 Modules --Right Cones in Groups --On Extensions of Regular Rings.ISBN: OCLC Number: Description: vi, pages: illustrations ; 24 cm.

Contents: Kasch Modules / T. Albu and R. Wisbauer --Compactness in Categories and Interpretations / P.

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N. Anh and R. Wiegandt --A Ring of Morita Context in Which Each Right Ideal is Weakly Self-injective / S. Barthwal, S. K. Jain and S.

Jhingan --Splitting.1. Preliminaries on module theory. Equivalences and dualities of categories. 2. Rings of matrices.

Equivalences of module categories. Generators and Morita contexts. Morita theorem. 3. Cogenerators. Pontryagin duality. Morita duality. 4. Classes of modules closed under different constructions (epimorphisms, direct sums etc.). (Pre)torsion classes.