Results 141 to 150 of about 708,128 (192)

Fuzzy Ideals of Artinian Rings

Fuzzy Sets and Systems, 1990
Main 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
exaly   +2 more sources

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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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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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
openaire   +3 more sources