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Distributed termination on a ring
BIT, 1986zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Heikki Saikkonen, Stefan Rönn
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On distributive modules and rings
Results in Mathematics, 2003Let \(R\) be an associative ring with identity element. A right \(R\)-module \(M\) is said to be `distributive' if its lattice of submodules is distributive. G. M. Brodski proved in 1997 that \(M\) is distributive if and only if \(M\) has no subfactors of the form \(K\oplus N\), where \(K\) and \(N\) are isomorphic nonzero modules.
Ferrero, Miguel, Sant'Ana, Alveri
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Hereditary and Semiperfect Distributive Rings
Algebra Colloquium, 2006A ring R is called right distributive if its lattice of right ideals is distributive. In this paper, we investigate distributive rings. We prove that if a ring R is right hereditary, then R is right distributive if and only if R is weakly right duo. We also prove that right semiperfect right distributive rings are right quasi-continuous.
Hong, Chan Yong +2 more
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Distributed exploration of dynamic rings
Distributed Computing, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Di Luna G +3 more
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On Annelidan, Distributive, and Bézout Rings
Canadian Journal of Mathematics, 2019AbstractA ring is called right annelidan if the right annihilator of any subset of the ring is comparable with every other right ideal. In this paper we develop the connections between this class of rings and the classes of right Bézout rings and rings whose right ideals form a distributive lattice.
Marks, Greg, Mazurek, Ryszard
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ℵ0-Distributive modules and rings
International Journal of Algebra and Computation, 2023Let A be a ring with minimum condition on principal right ideals. It is proved that countably distributive right (left) A-modules coincide with Artinian (Noetherian) right (left) A-modules. Rings, over which all right modules are [Formula: see text]-distributive coincide with rings of finite representation type.
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Rings of quotients and distributive rings
Russian Mathematical Surveys, 1990A ring \(R\) is said to be distributive (chain) if the lattices of left and right ideals are distributive (a chain). A distributive prime ring is an order in a chain prime ring. A distributive ring in which any two nonzero ideals have nonzero intersection is an order in a chain ring.
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Distributive non-localizable rings
Russian Mathematical Surveys, 2002Announcement of results. For details see e.g. the author's paper in J. Math. Sci., New York 114, No. 2, 1185-1203 (2003; Zbl 1046.16004).
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Mathematical Notes of the Academy of Sciences of the USSR, 1984
Let R be an associative ring with identity. R is said to be right distributive - or right arithmetical - (resp. right chain) if the lattice of right ideals is distributive (resp. is a chain). The main result of this paper is the following: R is a noetherian right distributive ring if and only if R is isomorphic to a finite direct product of artinian ...
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Let R be an associative ring with identity. R is said to be right distributive - or right arithmetical - (resp. right chain) if the lattice of right ideals is distributive (resp. is a chain). The main result of this paper is the following: R is a noetherian right distributive ring if and only if R is isomorphic to a finite direct product of artinian ...
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Bezout Rings, Polynomials, and Distributivity
Mathematical Notes, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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