Search Results

Now showing 1 - 2 of 2

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?
Citation - WoS: 14
Citation - Scopus: 12
Injective modules over down-up algebras
(Cambridge University Press, 2010) Carvalho, Paula A.A.B.; Lomp, Christian; Pusat, Dilek
The purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras A(α, β, γ) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple A(α, β, γ)-modules are locally Artinian provided the roots of X2 − αX − β are distinct roots of unity or both equal to 1.

Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection