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Fuzzy Ideals of Artinian Rings
Fuzzy Sets and Systems, 1990Main result: A ring R with unity is Artinian iff every of its fuzzy ideals I: \(R\to [0,1]\) is finitely valued. The author discusses also a few related results of \textit{T. K. Mukherjee}, \textit{M. K. Sen} [ibid. 21, 99-104 (1987; Zbl 0617.13001)] and \textit{F. Z. Pan} [ibid. 21, 105-113 (1987; Zbl 0616.16013)].
D S Malik
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A Condition for Artinian Rings to be Noetherian
Canadian Journal of Mathematics, 1978 Throughout this paper the word “Artinian (Noetherian) ring” means an associative ring with minimum (maximum) condition on left ideals. According to C. Hopkins, an Artinian ring is Noetherian if it contains a left or right identity [3, p. 728]. However we shall consider Artinian rings without the assumption of existence of such an identity, and the ...
Ichiro Murase
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Certain Artinian Rings are Noetherian
Canadian Journal of Mathematics, 1972 Throughout this paper the word “ring” will mean an associative ring which need not have an identity element. There are Artinian rings which are not Noetherian, for example C(p∞) with zero multiplication. These are the only such rings in that an Artinian ring
Robert C. Shock
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S-Artinian Rings and Finitely S-Cogenerated Rings [PDF]
Journal of Algebra and Its Applications, 2020 Let R be a commutative ring with nonzero identity and S subset of R be a multiplicatively closed subset. In this paper, we study S-Artinian rings and finitely S-cogenerated rings.
Unsal Tekir +2 more
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A Note on Compactifying Artinian Rings
Canadian Journal of Mathematics, 1974 In this note a number of compactifications are discussed within the class of artinian rings. In [1] the following was proved:Theorem. For an artinian ring R the following are equivalent:(1) R is equationally compact.(2) R+ ≃ B ⊕ P, where B is a finite group, P is a finite direct sum of Prüfer groups, and R · P = P · R = {0}.(3) R is a retract of a ...
David K. Haley
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Journal of Algebra and Its Applications, 2013
Let R be a ring, R is called a right ACS ring if the right annihilator of each element is essential in a direct summand of R. We prove that right CF ring is right artinian under right ACS condition. In particular, FGF conjecture is true under right ACS condition.
Li, Wenxi, Chen, Jianlong
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Let R be a ring, R is called a right ACS ring if the right annihilator of each element is essential in a direct summand of R. We prove that right CF ring is right artinian under right ACS condition. In particular, FGF conjecture is true under right ACS condition.
Li, Wenxi, Chen, Jianlong
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Semigroup Forum, 1998
Let \(F\) be a field, let \(G\) be a groupoid and let \(FG\) be a corresponding groupoid algebra. The author proves the following interesting theorems. There exists a groupoid \(H\) containing \(G\) as a subgroupoid and such that \(FH\) has three right ideals only.
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Let \(F\) be a field, let \(G\) be a groupoid and let \(FG\) be a corresponding groupoid algebra. The author proves the following interesting theorems. There exists a groupoid \(H\) containing \(G\) as a subgroupoid and such that \(FH\) has three right ideals only.
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