Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 1Citation - Scopus: 1Stability in Commutative Rings(TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2020) Ay Saylam, BaşakLet 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 Citation - WoS: 16Citation - Scopus: 14Rings Whose Modules Are Weakly Supplemented Are Perfect. Applications To Certain Ring Extensions(Mathematica Scandinavica, 2009) Büyükaşık, Engin; Lomp, ChristianIn 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.