Results 241 to 250 of about 1,070 (271)

Distributive and Semihereditary Rings

Journal of Mathematical Sciences, 2005
Let \(A\) be an associative ring with non-zero identity element, \(M\) be a right \(A\)-module, and \(n\) be a positive integer. The module \(M\) is called \(n\)-injective if for any \(n\)-generated right ideal \(B\) of \(A\) every homomorphism \(B_A\to M_A\) can be extended to a homomorphism \(A_A\to M_A\).
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On Annelidan, Distributive, and Bézout Rings

Canadian Journal of Mathematics, 2019
AbstractA 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, 2023
Let 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, 1990
A 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, 2002
Announcement 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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Distributive rings

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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Bezout Rings, Polynomials, and Distributivity

Mathematical Notes, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Distributive and Multiplication Modules and Rings

Mathematical Notes, 2004
All rings are assumed to be associative and to have non-zero identity. An \(A\)-module \(M\) is called a: (i) distributive module (for brevity, d-module) if the lattice of its submodules is distributive; (ii) multiplication module (for brevity, m-module) if for every submodule \(N\) of \(M\) there exists an ideal \(B\) of \(A\) such that \(N=MB\).
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Rings of elementary divisors and distributive rings

Russian Mathematical Surveys, 1991
See the review in Zbl 0767.16001.
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Distributively generated rings and distributive modules

Mathematical Notes, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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