ویراساینس.
سند علمی

Generalized lifting modules

Yongduo Wang, Nanqing Ding

چکیده

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 only if it isN ′-lifting andN ′′-lifting; (2) ifM is a Noetherianmodule, then M is lifting if and only if M is R-lifting if and only if M is an amply supplemented SSRS-module; and (3) letM be an amply supplemented SSRS-module such that Rad(M) is finitely generated, then M = K ⊕K ′, where K is a radical module and K ′ is a lifting module.

اسناد مشابه

  • Generalized lifting modules

    مقاله‌ی دسترسی آزاد۲۰۰۶International Journal of Mathematics and Mathematical SciencesYongduoWang, NanqingDing

  • A new generalization of t-lifting modules

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    In this paper we introduce the concept of $tCC$-modu\-les which is a proper generalizationof ($t$-)lifting modules. Let $M$ be a module over a ring $R$.We call $M$ a $tCC$-module(related to $t$-coclosed submodules) provided that for every$t$-coclosed submodule $N$ of $M$, there e

  • generalizations of delta-lifting modules

    مقاله۲۰۱۳journal of algebraic systemsyahya talebi, mehrab hosseinpour

    in this paper we introduce the notions of g∗l-module and g∗l-module whichare two proper generalizations of δ-lifting modules. we give some characteriza tions and properties of these modules. we show that a g∗l-module decomposesinto a semisimple submodule m1 and a submodule m2 of

  • 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

  • GENERALIZATIONS OF δ-LIFTING MODULES

    مقاله۲۰۱۳Journal of Algebraic SystemsYahya Talebi, Mehrab Hosseinpour

    In this paper we introduce the notions of $G_{1}^{*}L$-module and $G_{2}^{*}L$-module which are two proper generalizations of $\delta$-lifting modules. We give some characterizations and properties of these modules. We show that a$G_{2}^{*}L$-module decomposes into a semisimple s

  • On strongly PI-lifting modules

    مقاله۲۰۲۱Caspian Journal of Mathematical SciencesYeliz Kara

    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