Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Access Right: Open AccessSubject: search.filters.subject.Rings (Algebra)

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Stability in Commutative Rings
    (TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2020) Ay Saylam, Başak
    Let R be a commutative ring with zero-divisors and I an ideal of R. I is said to be ES-stable if JI = $I^2$ for some invertible ideal J ? I , and I is said to be a weakly ES-stable ideal if there is an invertible fractional ideal J and an idempotent fractional ideal E of R such that I = JE . We prove useful facts for weakly ES-stability and investigate this stability in Noetherian-like settings. Moreover, we discuss a question of A. Mimouni on locally weakly ES-stable rings: is a locally weakly ES-stable domain of finite character weakly ES-stable?
  • Article
    On pseudo semisimple rings
    (World Scientific Publishing Co. Pte Ltd, 2013) Büyükaşık, Engin; Mohamed, Saad H.; Mutlu, Hatice
    A necessary and sufficient condition is obtained for a right pseudo semisimple ring to be left pseudo semisimple. It is proved that a right pseudo semisimple ring is an internal exchange ring. It is also proved that a right and left pseudo semisimple ring is an SSP ring
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    Strongly Radical Supplemented Modules
    (Springer Verlag, 2012) Büyükaşık, Engin; Türkmen, Ergül
    Zöschinger studied modules whose radicals have supplements and called these modules radical supplemented. Motivated by this, we call a module strongly radical supplemented (briefly srs) if every submodule containing the radical has a supplement. We prove that every (finitely generated) left module is an srs-module if and only if the ring is left (semi)perfect. Over a local Dedekind domain, srs-modules and radical supplemented modules coincide. Over a nonlocal Dedekind domain, an srs-module is the sum of its torsion submodule and the radical submodule. © 2012 Springer Science+Business Media, Inc
  • Article
    Citation - WoS: 16
    Citation - Scopus: 14
    Rings Whose Modules Are Weakly Supplemented Are Perfect. Applications To Certain Ring Extensions
    (Mathematica Scandinavica, 2009) Büyükaşık, Engin; Lomp, Christian
    In this note we show that a ring R is left perfect if and only if every left R-module is weakly supplemented if and only if R is semilocal and the radical of the countably infinite free left R-module has a weak supplement.