ویراساینس.
مقاله

On strongly PI-lifting modules

Yeliz Kara

چکیده

In this paper, the class of strongly PI-lifting modules is introduced and investigated. The connections between strongly PI-lifting modules and the generalizations of lifting modules are presented. We provide that the class of strongly PI-lifting modules is contained in the class of PI-lifting modules. Moreover, it is proved that for an Abelian ring R, R is PI-lifting as a right R-module if and only if R=I has a projective cover for every right ideal I of R.The structural properties of strongly PI-lifting modules are determined, and examples are provided to exhibit and delimit our results.

اسناد مشابه

  • On strong liftings for projective limits

    سند علمی۲۰۰۷N. D. Mache, N. D. Macheras, W. Strauss

    We discuss the permanence of strong liftings under the formation of projective limits. The results are based on an appropriate consistency condition of the liftings with the projective system called “self-consistency”, which is fulfilled in many situations. In addition, we study

  • Generalized lifting modules

    سند علمی۲۰۰۶Int. J. Math. Mathematical SciencesYongduo Wang, Nanqing Ding

    We introduce the concepts of lifting modules and (quasi-)discrete modules relative to a given left module. We also introduce the notion of SSRS-modules. It is shown that (1) if M is an amply supplementedmodule and 0→N ′ →N →N ′′ → 0 an exact sequence, then M isN-lifting if and on

  • e-lifting modules relative to fully invariant submodules

    مقاله۲۰۱۹Journal of Algebra and Related TopicsF. Alizadeh, M. Hosseinpour, Z. Kamali

    In this paper, we introduce the notion FI-e-lifting modules which is a proper generalization of lifting (e-lifting) modules.Then we give some characterizations and properties of e-lifting and FI-e-lifting modules. We provide a decomposition of any e-lifting modules. It is shown t

  • Strongly Hollow R - Annihilator Lifting Modules and Strongly R - Annihilator (Hollow- Lifting) Modules

    مقاله‌ی دسترسی آزاد۲۰۲۰Iraqi Journal of ScienceOmar K.Ibrahim, Alaa A.Elewi

  • Relatively lifting modules

    سند علمی۲۰۰۷Septimiu Crivei, Nanqing Ding

    We consider a generalization of lifting modules relative to a class A of modules and a proper class E of short exact sequences of modules. These modules will be called E-A-lifting. We establish characterizations of modules with the property that every direct sum of copies of them

  • LIFTING MODULES WITH RESPECT TO A PRERADICAL

    مقاله۲۰۱۴Journal of Algebraic SystemsT. Amouzegar

    Let $M$ be a right module over a ring $R$, $tau_M$ a preradical on $sigma[M]$, and $Ninsigma[M]$. In this note we show that if $N_1, N_2in sigma[M]$ are two $tau_M$-lifting modules such that $N_i$ is $N_j$-projective ($i,j=1,2$), then $N=N_1oplus N_2$ is $tau_M$-lifting. We inves