[PDF] Top 20 On some classes of modules and their endomorphism rings

... In order to prove that the monoid homomorphism V (π) : V (S) → V (S/I ) is surjective, notice that I ⊇ J (S) and S/J (S) is Von Neumann regular, so that S/I is Von Neumann regular. Thus every finitely generated ... See full document

... symmetric modules of which their endomorphism rings are symmetric, namely simple modules and vector ...Rickart modules and 1-epiretractable modules play an important role in this ... See full document

... important theorem of Swan 6, the problem arises to define and investigate characteristic classes for finitely generated modules over a commutative ring... These can then be interpreted a[r] ... See full document

... 3. Constructing minimal approximations and almost split maps via ladders In this section R will always be a noetherian commutative Henselian CM local ring with canonical module and with dim R ≤ 2 and C = add(M ) for ... See full document

... In dimension g > 3, where only general representations of abelian varieties are available (such as those given by theta functions), there is to the best of our knowledge no efficient method to draw points uniformly at ... See full document

... Diverse methods of “improvement” of preradicals are known, i.e. of the construction of nearest preradicals with the required properties. In the paper [48] these methods are systematized and supplemented, using various ... See full document

... give some examples of different classes of R-modules M such that G(M ) is an totally disconnected ...for some ideal I of ...co-semisimple modules, finitely generated modules and ... See full document

... for modules and rings to measure how far away a module is from having an infinite finite presentation and develop ways to compute the projective dimension of a module with a finite presented dimension and ... See full document

... give some equivalent properties and characterizations of δ-Hopfian ...semisimple rings in terms of δ-Hopfian modules and show that a ring R is semisimple if and only if every R-module is ...δ-Hopfian ... See full document

... The fact that Theorem 1.1 is a common generalisation of the results on diagram algebras mentioned above, has been one of the motivations for the present paper. Boltje and Danz showed recently in [1] that certain double ... See full document

... Free divisors are connected to numerous areas of mathematics, and have attracted intense interest recently. They are hypersurfaces in (complex) manifolds and are typically not normal, and may even be reducible. For a ... See full document

... nil rings are Jacobson ...were some historical notes on nil ideals and nil radicals due to Amitsur ...graded rings were introduced and investigated by Jespers et al ...graded rings due to ... See full document

... Modules arise when the representing subjects have an additive structure: representations as endomorphisms of abelian groups and vector spaces are the main cases. A representation of a group G over a field K is the ... See full document

... Abstract. We consider Baer rings and Baer semisimple R-modules which are generalizations of semisimple modules. Sev- eral characterization theorems of Baer semisimple modules are ob- tained. ... See full document

... Gorenstein rings (R, m, k) with m 3 = 0 are known to be good, due to Sj¨odin [22]; see also Avramov, Iyengar, S¸ega ...local rings with m 4 = 0 can exhibit bad behavior, as there exist examples with µ(m) ≥ ... See full document

... Throughout the whole text, all rings are considered to be associative with unit 1 6= 0 and all modules are left unitary [5, 6]. Let R be a ring. The category of left R–modules will be denoted by ... See full document

... following classes of Galois extensions are given: (1) cen- trally projective Galois extensions (CP-Galois extensions), (2) faithfully Galois extensions, and (3) H-separable Galois ... See full document

... [25] and B.H. Neumann [22] considered rings in which addition need not be commutative. The first real structural theorems on near­ rings are due to D.W. Blackett [8], who in 1953 extended the theory of ... See full document

... 1. Introduction. Although the theory of linear difference equations over base fields is well understood, the theory over arbitrary ground rings and modules is still under development. It is becoming more ... See full document

... By [10, 19.9.1], the homotopy inverse limit of R is the inverse limit of a fibrant replace- ment of R in the diagram-injective model category of D-diagrams of ring spectra. This model structure exists by [11, 5.1.3]; see ... See full document